Ricci Curvature and Functional Inequalities for Interacting Particle Systems

Explore Ricci curvature bounds and their applications to interacting particle systems in this 45-minute lecture by Max Fathi. Delve into the concept of entropic Ricci curvature, introduced by M. Erbar, J. Maas, and A. Mielke, and discover how these bounds can be used to prove functional inequalities such as spectral gap bounds and modified logarithmic Sobolev inequalities. Examine the case of nonnegative curvature and its implications for measuring convergence rates to equilibrium in underlying dynamics. Learn about Markov chain examples, canonical examples, and simple random walks as applications of this theory. Follow the progression from introduction to clinical results and proofs, gaining insights into this advanced mathematical topic presented at the Hausdorff Center for Mathematics.

Introduction
Ricci curvature and functional inequalities
Pro
Markov chain examples
Questions
Properties
Canonical example
Simple random walk
Applications
Convergence
Clinical results
Proof