Entropic Ricci curvature bounds for discrete interacting systems

M. Fathi, J. Maas, The Annals of Applied Probability 26 (2016) 1774–1806.


Journal Article | Published | English
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Department
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.
Publishing Year
Date Published
2016-06-01
Journal Title
The Annals of Applied Probability
Acknowledgement
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.
Volume
26
Issue
3
Page
1774 - 1806
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Cite this

Fathi M, Maas J. Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability. 2016;26(3):1774-1806. doi:10.1214/15-AAP1133
Fathi, M., & Maas, J. (2016). Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability, 26(3), 1774–1806. https://doi.org/10.1214/15-AAP1133
Fathi, Max, and Jan Maas. “Entropic Ricci Curvature Bounds for Discrete Interacting Systems.” The Annals of Applied Probability 26, no. 3 (2016): 1774–1806. https://doi.org/10.1214/15-AAP1133.
M. Fathi and J. Maas, “Entropic Ricci curvature bounds for discrete interacting systems,” The Annals of Applied Probability, vol. 26, no. 3, pp. 1774–1806, 2016.
Fathi M, Maas J. 2016. Entropic Ricci curvature bounds for discrete interacting systems. The Annals of Applied Probability. 26(3), 1774–1806.
Fathi, Max, and Jan Maas. “Entropic Ricci Curvature Bounds for Discrete Interacting Systems.” The Annals of Applied Probability, vol. 26, no. 3, Institute of Mathematical Statistics, 2016, pp. 1774–806, doi:10.1214/15-AAP1133.

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