---
_id: '1448'
abstract:
- lang: eng
text: 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.
acknowledgement: "Supported by the German Research Foundation through the Collaborative
Research Center 1060\r\nThe 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. "
author:
- first_name: Max
full_name: Fathi, Max
last_name: Fathi
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: 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
apa: Fathi, M., & Maas, J. (2016). Entropic Ricci curvature bounds for discrete
interacting systems. The Annals of Applied Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/15-AAP1133
chicago: Fathi, Max, and Jan Maas. “Entropic Ricci Curvature Bounds for Discrete
Interacting Systems.” The Annals of Applied Probability. Institute of Mathematical
Statistics, 2016. https://doi.org/10.1214/15-AAP1133.
ieee: M. Fathi and J. Maas, “Entropic Ricci curvature bounds for discrete interacting
systems,” The Annals of Applied Probability, vol. 26, no. 3. Institute
of Mathematical Statistics, pp. 1774–1806, 2016.
ista: Fathi M, Maas J. 2016. Entropic Ricci curvature bounds for discrete interacting
systems. The Annals of Applied Probability. 26(3), 1774–1806.
mla: 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.
short: M. Fathi, J. Maas, The Annals of Applied Probability 26 (2016) 1774–1806.
date_created: 2018-12-11T11:52:05Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2021-01-12T06:50:49Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/15-AAP1133
intvolume: ' 26'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1501.00562
month: '06'
oa: 1
oa_version: Preprint
page: 1774 - 1806
publication: The Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '5748'
quality_controlled: '1'
scopus_import: 1
status: public
title: Entropic Ricci curvature bounds for discrete interacting systems
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 26
year: '2016'
...