Weighted Nash Inequalities (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan, Maheux, Patrick
Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and...
Weighted Nash Inequalities (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan, Maheux, Patrick
Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and...
Weighted Nash Inequalities (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan, Maheux, Patrick
Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and...
Dimension dependent hypercontractivity for Gaussian kernels (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan
We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties...
Dimension dependent hypercontractivity for Gaussian kernels (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan
We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties...
Dimension dependent hypercontractivity for Gaussian kernels (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan
We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties...
Dimension dependent hypercontractivity for Gaussian kernels (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan
We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties...
Weighted Nash Inequalities (2010)
Bakry, Dominique, Bolley, François, Gentil, Ivan
Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
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...
The hypergroup property and representation of Markov kernels (2008)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
The hypergroup property and representation of Markov kernels (2008)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
The hypergroup property and representation of Markov kernels (2008)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
On gradient bounds for the heat kernel on the Heisenberg group (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its Lévy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
The hypergroup property and representation of Markov kernels (2008)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
The hypergroup property and representation of Markov kernels (2008)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
Subelliptic Li-Yau estimates on three dimensional model spaces (2008)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Qian, Bin
We describe three elementary models in three dimensional subelliptic geometry which corresponds to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
On gradient bounds for the heat kernel on the Heisenberg group (2007)
Bakry, Dominique, Baudoin, Fabrice, Bonnefont, Michel, Chafai, Djalil
It is known that the couple formed by the two dimensional Brownian motion and its L\'evy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. The...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare (2007)
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...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)
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...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)
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...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)
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...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)
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...
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare. (2007)
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 logarithmic Sobolev form of the Li-Yau parabolic inequality (2006)
Bakry , Dominique, Ledoux , Michel
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
The hypergroup property and representation of Markov kernels (2006)
Bakry, Dominique, Huet, Nolwen
In a number of situations, Markov operators appear to be a wonderful tool to provide useful information on measured spaces, such as functional inequalities of the Sobolev-type. In this article, we...
The hypergroup property and representation of Markov kernels (2006)
Bakry, Dominique, Huet, Nolwen
In a number of situations, Markov operators appear to be a wonderful tool to provide useful information on measured spaces, such as functional inequalities of the Sobolev-type. In this article, we...
The hypergroup property and representation of Markov kernels (2006)
Bakry, Dominique, Huet, Nolwen
In a number of situations, Markov operators appear to be a wonderful tool to provide useful information on measured spaces, such as functional inequalities of the Sobolev-type. In this article, we...
The hypergroup property and representation of Markov kernels (2006)
Bakry, Dominique, Huet, Nolwen
In a number of situations, Markov operators appear to be a wonderful tool to provide useful information on measured spaces, such as functional inequalities of the Sobolev-type. In this article, we...
The hypergroup property and representation of Markov kernels (2006)
Bakry, Dominique, Huet, Nolwen
For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup...
A logarithmic Sobolev form of the Li-Yau parabolic inequality (2006)
Bakry, Dominique, Ledoux, Michel
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
Functional Inequalities for Markov semigroups (2006)
In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We...
Functional Inequalities for Markov semigroups (2006)
In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We...
A logarithmic Sobolev form of the Li-yau parabolic inequality (2006)
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
A logarithmic Sobolev form of the Li-yau parabolic inequality (2006)
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
Perturbations of Functional Inequalities Using Growth Conditions ∗ (2006)
Dominique Bakry, Michel Ledoux, Feng-yu Wang
Perturbations of functional inequalities are studied by using merely growth conditions in terms of a distance-like reference function. As a result, optimal sufficient conditions are obtained for...
A logarithmic Sobolev form of the Li-yau parabolic inequality (2006)
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
Functional Inequalities for Markov semigroups (2006)
In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We...
A logarithmic Sobolev form of the Li-yau parabolic inequality (2006)
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
Functional Inequalities for Markov semigroups (2006)
In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We...
A logarithmic Sobolev form of the Li-yau parabolic inequality (2006)
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau...
Functional Inequalities for Markov semigroups (2006)
In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We...
Volume comparison theorems without Jacobi fields (2005)
Bakry, Dominique, Qian, Zhongmin
Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which...
Volume comparison theorems without Jacobi fields (2005)
Bakry, Dominique, Qian, Zhongmin
Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which...
Extension of Bochner-Lichnérowicz formula on spheres (2005)
Bakry, Dominique, Ben-Taleb, Abdellatif
Given a second order differential operator L, we define the vector space of intrinsic bilinear operators associated with it. They are constructed only from the operator L itself and the algebra...
Extension of Bochner-Lichnérowicz formula on spheres (2005)
Bakry, Dominique, Ben-Taleb, Abdellatif
Given a second order differential operator L, we define the vector space of ”intrinsic bilinear operators” associated with it. They are constructed only from the operator L itself and the algebra...
Extension of Bochner-Lichnérowicz formula on spheres (2005)
Bakry, Dominique, Ben-Taleb, Abdellatif
Given a second order differential operator L, we define the vector space of ”intrinsic bilinear operators” associated with it. They are constructed only from the operator L itself and the algebra...
Volume comparison theorems without Jacobi fields (2005)
Bakry, Dominique, Qian, Zhongmin
Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which...
Extension of Bochner-Lichnérowicz formula on spheres (2005)
Bakry, Dominique, Ben-Taleb, Abdellatif
Given a second order differential operator L, we define the vector space of ”intrinsic bilinear operators” associated with it. They are constructed only from the operator L itself and the algebra...
Volume comparison theorems without Jacobi fields (2005)
Bakry, Dominique, Qian, Zhongmin
Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which...
Extension of Bochner-Lichnérowicz formula on spheres (2005)
Bakry, Dominique, Ben-Taleb, Abdellatif
Given a second order differential operator L, we define the vector space of ”intrinsic bilinear operators” associated with it. They are constructed only from the operator L itself and the algebra...
Volume comparison theorems without Jacobi fields (2005)
Bakry, Dominique, Qian, Zhongmin
Using a generalized curvature-dimension inequality and a new approach, we preset a differential inequality for an elliptic second order differential operator acting on distance functions, from which...
Harnack inequalities on a manifold with positive or negative Ricci curvature (1999)
Bakry, Dominique, Qian, Zhongmin M.
Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established....