Optimisation combinatoire (2010)
La méthode de la cavité en physique statistique a donné un nouvel élan à toute une classe de probèmes sur des structures combinatoires aléatoires. Les premiers succès remontent aux travaux G....
Spectrum of non-Hermitian heavy tailed random matrices (2010)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha
Spectrum of non-Hermitian heavy tailed random matrices (2010)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha
Spectrum of non-Hermitian heavy tailed random matrices (2010)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha
– Cost function F: R d → R reaching its minimum at x ∗. – Relation between the distance δ = |x−x ∗ | and the difference ǫ = F(x)− F(x ∗): if F is ”smooth”, ǫ(δ) = inf{F(x) −...
Spectrum of large random reversible Markov chains: two examples (2010)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior...
Spectrum of large random reversible Markov chains: two examples (2010)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior...
The rank of diluted random graphs (2009)
Bordenave, Charles, Lelarge, Marc, Salez, Justin
We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs converging locally to a Galton-Watson tree, we provide an explicit formula for the asymptotic...
Spectrum of large random reversible Markov chains: heavy tailed weights on the complete graph (2009)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K obtained by assigning i.i.d. non negative weights to the edges of the complete graph over n vertices, and normalizing by the corresponding row sum....
Spectrum of large random reversible Markov chains: heavy tailed weights on the complete graph (2009)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K obtained by assigning i.i.d. non negative weights to the edges of the complete graph over n vertices, and normalizing by the corresponding row sum....
Spectrum of large random reversible Markov chains: heavy tailed weights on the complete graph (2009)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K obtained by assigning i.i.d. non negative weights to the edges of the complete graph over n vertices, and normalizing by the corresponding row sum....
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Charles Bordenave, Venkat Anantharam
The adaptive control of Markovian stochastic processes has a mature theory, either for optimal discounted reward [3, 2] than for average reward [1]. However, the analysis of controlled particles...
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We consider the random reversible Markov kernel K on the complete graph with n vertices obtained by putting i.i.d. positive weights of law L on the n(n+1)/2 edges of the graph and normalizing each...
Load optimization in a planar network (2009)
Bordenave, Charles, Torrisi, Giovanni Luca
We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object...
de recherche Random Multi-access Algorithms- A Mean Field analysis (2008)
Charles Bordenave, David Mcdonald Alex, Re Proutière, Charles Bordenave, David Mcdonald, Re Proutière, ...
apport
On the birth-and-assassination process, with an application to scotching a rumor in a network (2008)
Bordenave, Charles; Université De Toulouse & CNRS; Charles.bordenave@math.univ-toulouse.fr
We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has a heavy-tailed distribution. We also establish that this process is a...
Spectrum of large random reversible Markov chains: two examples (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior...
Asymptotic stability region of slotted-Aloha (2008)
Bordenave, Charles, McDonald, David, Proutiere, Alexandre
We analyze the stability of standard, buffered, slotted-Aloha systems. Specifically, we consider a set of $N$ users, each equipped with an infinite buffer. Packets arrive into user $i$'s buffer...
de recherche Random Multi-access Algorithms- A Mean Field analysis (2008)
Charles Bordenave, David Mcdonald Alex, Re Proutière, Charles Bordenave, David Mcdonald, Re Proutière, ...
apport
Circular Law Theorem for Random Markov Matrices (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained...
Circular Law Theorem for Random Markov Matrices (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained...
Circular Law Theorem for Random Markov Matrices (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained...
On the birth-and-assassination process, with an application to scotching a rumor in a network (2008)
We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has an heavy-tailed distribution. We also establish that this process is a...
Spectrum of large random reversible Markov chains (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both...
Spectrum of large random reversible Markov chains (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both...
Spectrum of large random reversible Markov chains (2008)
Bordenave, Charles, Caputo, Pietro, Chafai, Djalil
In this work, we adopt a Random Matrix Theory point of view to study the spectrum of large reversible Markov chains in random environment. As the number of states tends to infinity, we consider both...
Resolvent of Large Random Graphs (2007)
Bordenave, Charles, Lelarge, Marc
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for...
Aldous, David J., Bordenave, Charles, Lelarge, Marc
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given...
Optimal control of interacting particle systems (2007)
Bordenave, Charles, Anantharam, Venkat
We analyze the optimal control of interacting particle systems, either for optimal discounted reward, than for average reward. We illustrate our results on some examples.
Optimal control of interacting particle systems (2007)
Bordenave, Charles, Anantharam, Venkat
We analyze the optimal control of interacting particle systems, either for optimal discounted reward, than for average reward. We illustrate our results on some examples.
Large deviations of Poisson cluster processes (2007)
Bordenave, Charles, Torrisi, Giovanni Luca
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes...
The radial spanning tree of a Poisson point process (2007)
Baccelli, Francois, Bordenave, Charles
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We...
The radial spanning tree of a Poisson point process (2007)
Baccelli, Francois, Bordenave, Charles
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We...
Bordenave, Charles, McDonald, David, Proutiere, Alexandre
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps...
Optimal control of interacting particle systems (2007)
Bordenave, Charles, Anantharam, Venkat
We analyze the optimal control of interacting particle systems, either for optimal discounted reward, than for average reward. We illustrate our results on some examples.
Optimal control of interacting particle systems (2007)
Bordenave, Charles, Anantharam, Venkat
We analyze the optimal control of interacting particle systems, either for optimal discounted reward, than for average reward. We illustrate our results on some examples.
Optimal control of interacting particle systems (2007)
Bordenave, Charles, Anantharam, Venkat
We analyze the optimal control of interacting particle systems, either for optimal discounted reward, than for average reward. We illustrate our results on some examples.
A Random Multiple Access Protocol with Spatial Interactions (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
We analyse an ALOHA-type random multiple-access protocol where users have local interactions. We show that the fluid model of the system workload satisfies a certain differential equation. We obtain...
Near-Minimal Spanning Trees: a Scaling Exponent in Probability Models (2006)
Aldous, David, Bordenave, Charles, Lelarge, Marc
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must...
Analyse stochastique des réseaux spatiaux. (2006)
Les réseaux spatiaux sont des réseaux dans lesquels les sommets occupent une position dans l'espace Euclidien. Les interactions dans ces réseaux sont déterminées par cette géometrie...
Analyse stochastique des réseaux spatiaux. (2006)
Les réseaux spatiaux sont des réseaux dans lesquels les sommets occupent une position dans l'espace Euclidien. Les interactions dans ces réseaux sont déterminées par cette géometrie...
Analyse stochastique des réseaux spatiaux. (2006)
Les réseaux spatiaux sont des réseaux dans lesquels les sommets occupent une position dans l'espace Euclidien. Les interactions dans ces réseaux sont déterminées par cette géometrie...
Eigenvalues of Euclidean Random Matrices (2006)
We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$....
The dead leaves model: a general tessellation modeling occlusion (2006)
Bordenave, Charles, Gousseau, Yann, Roueff, François
In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the mathematical morphology school, is defined as a sequential...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from one point to another. The set of paths leading to a given point defines a tree known as the navigation tree. In...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this...
Un Protocole d'Accès Multiple Aléatoire avec Interactions Spatiales (2006)
Bordenave, Charles, Foss, Serguei, Shneer, Vsevolod
Nous étudions un protocole d'accès de type aloha où les utilisateurs ont des interactions locales. Nous établissons que le modèle fluide de la charge du système satisfait une équation...
Eigenvalues of Euclidean Random Matrices (2006)
Nous étudions la mesure spectrale de grande matrices aléatoires Euclidiennes. Les entrées de ces matrices sont déterminées par la position relative de $n$ points aléatoires dans un ensemble...
Navigation on a Poisson point process (2006)
On a locally finite point set, a navigation defines a path through the point set from a point to an other. The set of paths leading to a given point defines a tree, the navigation tree. In this...
The Radial Spanning Tree of a Poisson Point Process (2005)
Baccelli, François, Bordenave, Charles
We analyze a class of random spanning trees built on a realization of an homogeneous Poisson point process of the plane. This tree has a local construction rule and a radial structure with the origin...
Random Multi-access Algorithms - A Mean Field analysis (2005)
Bordenave, Charles, Mcdonald, David, Proutière, Alexandre
In this paper, using mean field techniques, we present a performance analysis of random back-off algorithms, such as the exponential back-off algorithm, in the case of a finite number of saturated...
The Radial Spanning Tree of a Poisson Point Process (2005)
Baccelli, François, Bordenave, Charles
We analyze a class of random spanning trees built on a realization of an homogeneous Poisson point process of the plane. This tree has a local construction rule and a radial structure with the origin...
Random Multi-access Algorithms - A Mean Field analysis (2005)
Bordenave, Charles, Mcdonald, David, Proutière, Alexandre
In this paper, using mean field techniques, we present a performance analysis of random back-off algorithms, such as the exponential back-off algorithm, in the case of a finite number of saturated...
The Radial Spanning Tree of a Poisson Point Process (2005)
Baccelli, François, Bordenave, Charles
We analyze a class of random spanning trees built on a realization of an homogeneous Poisson point process of the plane. This tree has a local construction rule and a radial structure with the origin...
Random Multi-access Algorithms - A Mean Field analysis (2005)
Bordenave, Charles, Mcdonald, David, Proutière, Alexandre
In this paper, using mean field techniques, we present a performance analysis of random back-off algorithms, such as the exponential back-off algorithm, in the case of a finite number of saturated...
Random Multi-access Algorithms - A Mean Field analysis (2005)
Bordenave, Charles, Mcdonald, David, Proutière, Alexandre
In this paper, using mean field techniques, we present a performance analysis of random back-off algorithms, such as the exponential back-off algorithm, in the case of a finite number of saturated...
The Radial Spanning Tree of a Poisson Point Process (2005)
Baccelli, François, Bordenave, Charles
We analyze a class of random spanning trees built on a realization of an homogeneous Poisson point process of the plane. This tree has a local construction rule and a radial structure with the origin...
Random Multi-access Algorithms - A Mean Field analysis (2005)
Bordenave, Charles, Mcdonald, David, Proutière, Alexandre
In this paper, using mean field techniques, we present a performance analysis of random back-off algorithms, such as the exponential back-off algorithm, in the case of a finite number of saturated...
The Radial Spanning Tree of a Poisson Point Process (2005)
Baccelli, François, Bordenave, Charles
We analyze a class of random spanning trees built on a realization of an homogeneous Poisson point process of the plane. This tree has a local construction rule and a radial structure with the origin...
Stability of spatial queueing systems (2004)
In this report, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at some points in space and the server...
Stability Properties of data flows on a CDMA network in macrodiversity (2004)
In this report, we analyze a general model of large CDMA networks (Code Division Multiple Access) and we propose a new formalism to represent the workload in wireless networks. We focus on stability...
Optimal Power Allocation in CDMA Networks with Macrodiversity (2004)
This report defines and analyzes a general model of macrodiversity in CDMA networks (Code Division Multiple Access). Some differences between the up link (from users to base stations) and downlink...
Stability of spatial queueing systems (2004)
In this report, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at some points in space and the server...
Stability Properties of data flows on a CDMA network in macrodiversity (2004)
In this report, we analyze a general model of large CDMA networks (Code Division Multiple Access) and we propose a new formalism to represent the workload in wireless networks. We focus on stability...
Optimal Power Allocation in CDMA Networks with Macrodiversity (2004)
This report defines and analyzes a general model of macrodiversity in CDMA networks (Code Division Multiple Access). Some differences between the up link (from users to base stations) and downlink...
Stability of spatial queueing systems (2004)
In this report, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at some points in space and the server...
Stability Properties of data flows on a CDMA network in macrodiversity (2004)
In this report, we analyze a general model of large CDMA networks (Code Division Multiple Access) and we propose a new formalism to represent the workload in wireless networks. We focus on stability...
Optimal Power Allocation in CDMA Networks with Macrodiversity (2004)
This report defines and analyzes a general model of macrodiversity in CDMA networks (Code Division Multiple Access). Some differences between the up link (from users to base stations) and downlink...
Optimal Power Allocation in CDMA Networks with Macrodiversity (2004)
This report defines and analyzes a general model of macrodiversity in CDMA networks (Code Division Multiple Access). Some differences between the up link (from users to base stations) and downlink...
Stability Properties of data flows on a CDMA network in macrodiversity (2004)
In this report, we analyze a general model of large CDMA networks (Code Division Multiple Access) and we propose a new formalism to represent the workload in wireless networks. We focus on stability...
Stability of spatial queueing systems (2004)
In this report, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at some points in space and the server...
Optimal Power Allocation in CDMA Networks with Macrodiversity (2004)
This report defines and analyzes a general model of macrodiversity in CDMA networks (Code Division Multiple Access). Some differences between the up link (from users to base stations) and downlink...
Stability Properties of data flows on a CDMA network in macrodiversity (2004)
In this report, we analyze a general model of large CDMA networks (Code Division Multiple Access) and we propose a new formalism to represent the workload in wireless networks. We focus on stability...
Stability of spatial queueing systems (2004)
In this report, we analyze a queueing system characterized by a space-time arrival process of customers served by a countable set of servers. Customers arrive at some points in space and the server...