Add to ORKGInternational audienceWe 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 no more uniformly convex. Proof is straightforward, simplifying deeply proofs of Carrillo-McCann-Villani \cite{CMV,CMV2} and completing results of Malrieu \cite{malrieu03} in the uniformly convex case. It relies on an uniform propagation of chaos property and a direct control in Wasserstein distance of solutions starting with different initial measures. The deviation inequality is obtained via a $T_1$ transportation cost inequality replacing the logarithmic Sobolev inequality which is no more clearly dimension free
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion pr...
33 pagesInternational audienceExistence and uniqueness of global in time measure solution for the mu...
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develo...
International audienceWe use here a particle system to prove a convergence result as well as a devia...
We use here a particle system to prove a convergence result as well as a deviation inequality for...
International audienceWe study the long time asymptotics of a nonlinear, nonlocal equation used in t...
The goal of the current paper is to provide information about the basins of attraction of the granul...
We introduce a new interacting particle system to investigate the behavior of the nonlinear, non-loc...
We investigate the exit problem for a diffusion which drift is not time-homogeneous. More precisely,...
The goal of the current paper is to provide information about the limiting probability of the granul...
International audienceThis article deals with a mean-field model. We consider a large number of part...
International audienceWe derive the porous medium equation from an interacting particle system which...
We obtain new a priori estimates for spatially inhomogeneous solutions of a kinetic equation for gr...
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a...
We consider the model of Directed Polymers in an i.i.d. gaussian or bounded Environment in the $L^2$...
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion pr...
33 pagesInternational audienceExistence and uniqueness of global in time measure solution for the mu...
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develo...
International audienceWe use here a particle system to prove a convergence result as well as a devia...
We use here a particle system to prove a convergence result as well as a deviation inequality for...
International audienceWe study the long time asymptotics of a nonlinear, nonlocal equation used in t...
The goal of the current paper is to provide information about the basins of attraction of the granul...
We introduce a new interacting particle system to investigate the behavior of the nonlinear, non-loc...
We investigate the exit problem for a diffusion which drift is not time-homogeneous. More precisely,...
The goal of the current paper is to provide information about the limiting probability of the granul...
International audienceThis article deals with a mean-field model. We consider a large number of part...
International audienceWe derive the porous medium equation from an interacting particle system which...
We obtain new a priori estimates for spatially inhomogeneous solutions of a kinetic equation for gr...
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a...
We consider the model of Directed Polymers in an i.i.d. gaussian or bounded Environment in the $L^2$...
In this paper we intend to give a comprehensive approach of functional inequalities for diffusion pr...
33 pagesInternational audienceExistence and uniqueness of global in time measure solution for the mu...
As a counterpoint to classical stochastic particle methods for linear diffusion equations, we develo...