128 citations · 197 across the 16 of their papers we have counts for
3 papers · 2 filters
Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
Matthias Erbar, Max Fathi
We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, bu…
Ricci curvature bounds for weakly interacting Markov chains
Matthias Erbar, Christopher Henderson, Georg Menz +1
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in…
Gradient flow structure for McKean-Vlasov equations on discrete spaces
Matthias Erbar, Max Fathi, Vaios Laschos +1
In this work, we show that a family of non-linear mean-field equations on discrete spaces can be viewed as a gradient flow of a natural free energy functional with respect to a cer…