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June 2013 Ricci curvature of Markov chains on Polish spaces revisited
Fu-Zhou Gong, Yuan Liu, Zhi-Ying Wen
Osaka J. Math. 50(2): 491-502 (June 2013).

Abstract

Recently, Y. Ollivier defined the Ricci curvature of Markov chains on Polish spaces via the contractivity of transition kernels under the $L^{1}$ Wasserstein metric. In this paper, we will discuss further the spectral gap, entropy decay, and logarithmic Sobolev inequality for the $\lambda$-range gradient operator. As an application, given resistance forms (i.e. symmetric Dirichlet forms with finite effective resistance) on fractals, we can construct Markov chains with positive Ricci curvature, which yields the Gaussian-then-exponential concentration of invariant distributions for Lipschitz test functions.

Citation

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Fu-Zhou Gong. Yuan Liu. Zhi-Ying Wen. "Ricci curvature of Markov chains on Polish spaces revisited." Osaka J. Math. 50 (2) 491 - 502, June 2013.

Information

Published: June 2013
First available in Project Euclid: 21 June 2013

zbMATH: 1283.60102
MathSciNet: MR3080812

Subjects:
Primary: 47D07, 60J10
Secondary: 28A80, 31C25

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics

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Vol.50 • No. 2 • June 2013
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