Entropic Ricci curvature bounds for discrete interacting systems Journal Article


Author(s): Fathi, Max; Maas, Jan
Article Title: Entropic Ricci curvature bounds for discrete interacting systems
Affiliation IST Austria
Abstract: We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli–Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.
Keywords: Bernoulli-Laplace model; Birthdeath processes; Discrete Ricci curvature; Functional inequalities; Random transposition model; Transport metrics; Zero-range processes
Journal Title: The Annals of Applied Probability
Volume: 26
Issue 3
ISSN: 1050-5164
Publisher: Institute of Mathematical Statistics  
Date Published: 2016-06-01
Start Page: 1774
End Page: 1806
URL:
DOI: 10.1214/15-AAP1133
Notes: Supported by the German Research Foundation through the Collaborative Research Center 1060 The Mathematics of Emergent Effects and the Hausdorff Center for Mathematics. Part of this work has been done while M. Fathi visited J. Maas at the University of Bonn in July 2014.We would like to thank the referees for their careful reading of the manuscript.
Open access: yes (repository)
IST Austria Authors
  1. Jan Maas
    25 Maas
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