114 citations · 295 across the 7 of their papers we have counts for
9 papers
Dynamics of a planar Coulomb gas
François Bolley, Djalil Chafai, Joaquín Fontbona
We study the long-time behavior of the dynamics of interacting planar Brow-nian particles, confined by an external field and subject to a singular pair repulsion. The invariant law…
Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction
François Bolley, José A. Carrillo
It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Und…
Dimensional contraction via Markov transportation distance
François Bolley, Ivan Gentil, Arnaud Guillin
It is now well known that curvature conditions à la Bakry-Emery are equivalent to contraction properties of the heat semigroup with respect to the classical quadratic Wasserstein d…
Uniform convergence to equilibrium for granular media
François Bolley, Ivan Gentil, Arnaud Guillin
We study the long time asymptotics of a nonlinear, nonlocal equation used in the modelling of granular media. We prove a uniform exponential convergence to equilibrium for degenera…
Mean-field limit for the stochastic Vicsek model
François Bolley, José A. Cañizo, José A. Carrillo
We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic m…
Dimension dependent hypercontractivity for Gaussian kernels
Dominique Bakry, François Bolley, Ivan Gentil
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 r…
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
Francois Bolley, Arnaud Guillin, Florent Malrieu
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilis…
Contractive metrics for scalar conservation laws
F. Bolley, Y. Brenier, G. Loeper
We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to t…
Quantitative concentration inequalities for empirical measures on non-compact spaces
Francois Bolley, Arnaud Guillin, Cedric Villani
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some erro…