Patrick Cattiaux

Some remarks on weighted logarithmic Sobolev inequality (2010)

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also...

Some remarks on weighted logarithmic Sobolev inequality (2010)

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also...

Functional inequalities for heavy tailed distributions and application to isoperimetry (2010)

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also...

Cattiaux, Patrick; Institut Mathématique De Toulouse; Patrick.cattiaux@math.univ-toulouse.fr, Gozlan, Nathael; Université Marne La Vallée; Nathael.gozlan@univ-mlv.fr, Guillin, Arnaud; Université Blaise Pascal; Guillin@math.univ-bpclermont.fr, Roberto, Cyril; Université Marne La Vallée; Cyril.roberto@univ-mlv.fr

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2010)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2010)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Poincaré inequality and the Lp convergence of semi-groups (2010)

Poincar\'e inequality and the Lp convergence of semi-groups (2010)

We prove that for symmetric Markov processes of diffusion type admitting a ``carré du champ'', the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in...

Poincaré inequality and the Lp convergence of semi-groups (2010)

We prove that for symmetric Markov processes of diffusion type admitting a "carr\'e du champ", the Poincar\'e inequality is equivalent to the exponential convergence of the associated semi-group in...

Functional Inequalities via Lyapunov conditions (2010)

We prove that for symmetric Markov processes of diffusion type admitting a ``carré du champ'', the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincar\'e inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Functional Inequalities via Lyapunov conditions (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2010)

We review here some recent results by the authors, and various coauthors, on (weak,super) Poincaré inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite...

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Functional inequalities for heavy tails distributions and application to isoperimetry (2010)

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

Functional inequalities for heavy tails distributions and application to isoperimetry (2010)

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

Poincaré inequality and the Lp convergence of semi-groups (2010)

Some remarks on weighted logarithmic Sobolev inequality (2010)

We prove that for symmetric Markov processes of diffusion type admitting a ``carré du champ'', the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in...

Functional inequalities for heavy tails distributions and application to isoperimetry (2010)

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also...

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

TRENDS TO EQUILIBRIUM IN TOTAL VARIATION DISTANCE (2009)

TRENDS TO EQUILIBRIUM IN TOTAL VARIATION DISTANCE (2009)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality (2009)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincaré and weak...

TRENDS TO EQUILIBRIUM IN TOTAL VARIATION DISTANCE (2009)

Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality (2009)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincaré and weak...

Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality (2009)

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincaré and weak...

Trends to equilibrium in total variation distance (2009)

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2008)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Competitive or Weak Cooperative Stochastic Lotka-Volterra Systems Conditioned to Non-Extinction (2008)

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

Functional inequalities for heavy tails distributions and application to isoperimetry (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

A simple proof of the Poincaré inequality for a large class of probability measures (2008)

Bakry, Dominique; LSP, Univ. Toulouse 3; Bakry@math.univ-toulouse.fr, Barthe, Franck; LSP, Univ. Toulouse 3; Barthe@math.univ-toulouse.fr, Cattiaux, Patrick; LSP, Univ. Toulouse 3; Cattiaux@math.univ-toulouse.fr, Guillin, Arnaud; LATP, Univ. Aix-Marseille 1; Guillin@cmi.univ-mrs.fr

Abstract. We give a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures on Rn. The proof...

Probabilistic approach for granular media equations in the non uniformly convex case. (2008)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Probabilistic approach for granular media equations in the non uniformly convex case. (2008)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Functional inequalities for heavy tails distributions and application to isoperimetry (2008)

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

Functional inequalities for heavy tails distributions and application to isoperimetry (2008)

Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril

This paper is devoted to the study of probability measures with heavy tails. Using the Lyapunov function approach we prove that such measures satisfy different kind of functional inequalities such as...

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2008)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2008)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Asymptotic analysis and diffusion limit of the Persistent Turning Walker Model (2008)

Cattiaux, Patrick, Chafai, Djalil, Motsch, Sébastien

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic...

Deviation bounds for additive functionals of Markov processes (2008)

Probabilistic approach for granular media equations in the non uniformly convex case. (2008)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

COMPETITIVE OR WEAK COOPERATIVE STOCHASTIC LOTKA-VOLTERRA SYSTEMS CONDITIONED TO NON-EXTINCTION (2008)

A note on Talagrand's transportation inequality and logarithmic Sobolev inequality (2008)

We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two...

Probabilistic approach for granular media equations in the non uniformly convex case. (2008)

We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand's transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient...

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Probabilistic approach for granular media equations in the non uniformly convex case. (2008)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Lyapunov conditions for logarithmic Sobolev and Super Poincar\'e inequality (2007)

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar\'e inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincar\'e and...

Isoperimetry between exponential and Gaussian (2007)

Barthe, Franck; Institut De Mathematiques; Barthe@math.ups-tlse.fr, Cattiaux, Patrick; Ecole Polytechnique Et MODALX; Cattiaux@cmapx.polytechnique.fr, Roberto, Cyril; Université De Marne La Vallée; Cyril.roberto@univ-mlv.fr

We study the isoperimetric problem for product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are...

Isoperimetry between exponential and Gaussian (2007)

Barthe, Franck; Institut De Mathematiques; Barthe@math.ups-tlse.fr, Cattiaux, Patrick; Ecole Polytechnique Et MODALX; Cattiaux@cmapx.polytechnique.fr, Roberto, Cyril; Université De Marne La Vallée; Cyril.roberto@univ-mlv.fr

We study the isoperimetric problem for product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions, that is, existence of a quasi-stationary distribution, conditional convergence to such a distribution,...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, Martin, Jaime San

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Trends to Equilibrium in Total Variation Distance (2007)

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare (2007)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

A criterion for Talagrand's quadratic transportation cost inequality (2007)

Weak logarithmic Sobolev inequalities and entropic convergence (2007)

We show that the quadratic transportation cost inequality $T_2$ is equivalent to both a Poincar\'e inequality and a strong form of the Gaussian concentration property. The main ingredient in the...

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

TRENDS TO EQUILIBRIUM IN TOTAL VARIATION DISTANCE (2007)

Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality (2007)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincaré and weak...

Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality (2007)

Cattiaux, Patrick, Guillin, Arnaud, Wang, Feng-Yu, Wu, Liming

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or $F$-Sobolev). The case of Poincaré and weak...

TRENDS TO EQUILIBRIUM IN TOTAL VARIATION DISTANCE (2007)

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

Weak logarithmic Sobolev inequalities and entropic convergence (2007)

Quasi-stationary distributions and diffusion models in population dynamics (2007)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Quasi-stationary distributions and diffusion models in population dynamics (2007)

Cattiaux, Patrick, Collet, Pierre, Lambert, Amaury, Martinez, Servet, Méléard, Sylvie, San Martin, Jaime

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an...

Weak logarithmic Sobolev inequalities and entropic convergence (2007)

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

Weak logarithmic Sobolev inequalities and entropic convergence (2007)

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

Weak logarithmic Sobolev inequalities and entropic convergence (2007)

Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Bakry, Dominique, Cattiaux, Patrick, Guillin, Arnaud

We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie, the second one...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry (2006)

Barthe , Franck, Cattiaux , Patrick, Roberto , Cyril

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Probabilistic approach for granular media equations in the non uniformly convex case. (2006)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Probabilistic approach for granular media equations in the non uniformly convex case. (2006)

Cattiaux, Patrick, Guillin, Arnaud, Malrieu, Florent

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Probabilistic approach for granular media equations in the non uniformly convex case (2006)

Cattiaux, Patrick, Arnaud, Guillin, Florent, Malrieu

We use here a particle system to prove a convergence result as well as a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are...

Deviation bounds for additive functionals of Markov processes (2006)

Deviation bounds for additive functionals of Markov process (2006)

In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some...

Isoperimetry between exponential and Gaussian (2006)

In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Deviation bounds for additive functionals of Markov processes (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Deviation bounds for additive functionals of Markov processes (2006)

In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some...

Isoperimetry between exponential and Gaussian (2006)

In this paper we derive non asymptotic deviation bounds for $$\P_\nu (|\frac 1t \int_0^t V(X_s) ds - \int V d\mu | \geq R)$$ where $X$ is a $\mu$ stationary and ergodic Markov process and $V$ is some...

Interpolatec inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Isoperimetry between exponential and Gaussian (2006)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Isoperimetry between exponential and Gaussian (2006)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Weak logarithmic Sobolev inequalities and entropic convergence (2005)

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate...

Weak logarithmic Sobolev inequalities and entropic convergence (2005)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner...

Weak logarithmic Sobolev inequalities and entropic convergence (2005)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Weak logarithmic Sobolev inequalities and entropic convergence (2005)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Hypercontractivity for perturbed diffusion semigroups (2005)

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Hypercontractivity for perturbed diffusion semigroups (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Deviations bounds and conditional principles for thin sets (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Hypercontractivity for perturbed diffusion semigroups (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Concentration for independent random variables with heavy tails (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Concentration for independent random variables with heavy tails (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Hypercontractivity for perturbed diffusion semigroups (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Hypercontractivity for perturbed diffusion semigroups (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Hypercontractivity for perturbed diffusion semigroups (2005)

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Hypercontractivity for perturbed diffusion semigroups (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Hypercontractivity for perturbed diffusion semigroups (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Hypercontractivity for perturbed diffusion semigroups (2005)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Deviations bounds and conditional principles for thin sets. (2005)

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are...

Concentration for independent random variables with heavy tails (2005)

The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. (2004)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

A criterion for Talagrand's quadratic transportation cost inequality (2003)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide...

Large deviations and variational theorems for marginal problems (1999)

We show that the quadratic transportation cost inequality $T_2$ is equivalent to both a Poincar\'e inequality and a strong form of the Gaussian concentration property. The main ingredient in the...

Cattiaux, Patrick, Gamboa, Fabrice

On a product probability space (E ×F, P), we give variational characterizations for the existence of a probability measure Q with given marginals, such that Q is absolutely continuous with respect...

Minimization of the Kullback information for some Markov processes (1996)

Cattiaux, Patrick, Léonard, Christian

Minimization of the Kullback information of diffusion processes (1994)

Cattiaux, Patrick, Léonard, Christian

Stochastic calculus and degenerate boundary value problems (1992)

Hypoellipticité et hypoellipticité partielle pour les diffusions avec une condition frontière (1986)