128 citations · 197 across the 16 of their papers we have counts for
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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…
A gradient flow approach to the Boltzmann equation
Matthias Erbar
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which…
Smoothing and non-smoothing via a flow tangent to the Ricci flow
Matthias Erbar, Nicolas Juillet
We study a transformation of metric measure spaces introduced by Gigli and Mantegazza consisting in replacing the original distance with the length distance induced by the transpor…
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…