3 citations · 5 across the 6 of their papers we have counts for
12 papers
Stability of eigenvalues and observable diameter in RCD spaces
Jérôme Bertrand, Max Fathi
We study stability of the spectral gap and observable diameter for metricmeasure spaces satisfying the RCD(1, ) condition. We show that if such a space has an almost maxima…
Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels
Max Fathi, Dan Mikulincer
We investigate stability of invariant measures of diffusion processes with respect to distances on the coefficients, under an assumption of log-concavity. The method is a var…
Self-improvement of the Bakry-Emery criterion for Poincar{é} inequalities and Wasserstein contraction using variable curvature bounds
Patrick Cattiaux, Max Fathi, Arnaud Guillin
We study Poincar{é} inequalities and long-time behavior for diffusion processes on R^n under a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estima…
Bounds on optimal transport maps onto log-concave measures
Maria Colombo, Max Fathi
We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz,…
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
Matthias Erbar, Max Fathi, André Schlichting
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics bas…
A proof of the Caffarelli contraction theorem via entropic regularization
Max Fathi, Nathael Gozlan, Maxime Prodhomme
We give a new proof of the Caffarelli contraction theorem, which states that the Brenier optimal transport map sending the standard Gaussian measure onto a uniformly log-concave pr…