114 citations · 295 across the 7 of their papers we have counts for
5 papers · 1 filter
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…
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…
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…