128 citations · 197 across the 16 of their papers we have counts for
10 papers · 1 filter
Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
Matthias Erbar, Martin Huesmann, Jonas Jalowy +1
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary rand…
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…
The one-dimensional log-gas free energy has a unique minimiser
Matthias Erbar, Martin Huesmann, Thomas Leblé
We prove that, at every positive temperature, the infinite-volume free energy of the one dimensional log-gas, or beta-ensemble, has a unique minimiser, which is the Sine-beta proce…
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…
From large deviations to Wasserstein gradient flows in multiple dimensions
Matthias Erbar, Jan Maas, Michiel Renger
We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peleti…
Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models
Matthias Erbar, Jan Maas, Prasad Tetali
We calculate a Ricci curvature lower bound for some classical examples of random walks, namely, a chain on a slice of the n-dimensional discrete cube (the so-called Bernoulli-Lapla…
Gradient flows of the entropy for jump processes
Matthias Erbar
We introduce a new transportation distance between probability measures that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou-Brenier formula.…
Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation
Matthias Erbar
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable pha…