255 citations · 949 across the 71 of their papers we have counts for
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Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition
François Bolley, Ivan Gentil, Arnaud Guillin +1
The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent…
From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules
Nicolas Fournier, Arnaud Guillin
We prove a quantitative result of convergence of a conservative stochastic particle system to the solution of the homogeneous Landau equation for hard potentials. There are two mai…
Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities
François Bolley, Ivan Gentil, Arnaud Guillin
In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Bra…
Transportation cost-information and concentration inequalities for bifurcating Markov chains
Siméon Valère Bitseki Penda, Mikael Escobar-Bach, Arnaud Guillin
We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models…