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We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below.
An optimal Poincaré inequality for convex domains
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A lower bound for the first eigenvalue of the Laplacian on a compact manifold
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A note on the isoperimetric constant
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On the estimate of the first eigenvalue of a compact Riemannian manifold
J.Q. Zhong and H.C. Yang · 1984
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Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
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Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
S. G. Bobkov and F. Götze · 1999
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Curvature of nonlocal markov generators
M. Schmuckenschläger · 1999
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Some new results on eigenvectors via dimension, diameter, and Ricci curvature
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The concentration of measure phenomenon
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Spectral gap for the zero range process with constant rate
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A remark on Zhong-Yang’s eigenvalue estimate
F. Hang and X. Wang · 2007
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Remarks on non-interacting conservative spin systems: the case of gamma distributions
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Markov chains and mixing times
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From concentration to logarithmic Sobolev and Poincaré inequalities
N. Gozlan, C. Roberto, and P.-M. Samson · 2011
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From concentration to isoperimetry: semigroup proofs
M. Ledoux · 2011
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Gradient flows of the entropy for finite Markov chains
J. Maas · 2011
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Ricci curvature of finite Markov chains via convexity of the entropy
M. Erbar and J. Maas · 2012
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On the convexity of the entropy along entropic interpolations
C. Léonard · 2013
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Geodesic convexity of the relative entropy in reversible Markov chains
A. Mielke · 2013
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Ricci curvature for metric-measure spaces via optimal transport
J. Lott and C. Villani · 2009
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On the role of convexity in functional and isoperimetric inequalities
E. Milman · 2009
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On the role of convexity in isoperimetry, spectral gap and concentration
E. Milman · 2009
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Ricci curvature of Markov chains on metric spaces
Y. Ollivier · 2009
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Optimal transport, Old and new
C. Villani · 2009
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Ricci curvature and eigenvalue estimate on locally finite graphs
Y. Lin and S.-T. Yau · 2010
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Analysis and geometry of Markov diffusion operators
D. Bakry, I. Gentil, and M. Ledoux · 2014
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Harnack inequalities for graphs with non-negative Ricci curvature
F. Chung, Y. Lin, and S.-T. Yau · 2014
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Displacement convexity of entropy and related inequalities on graphs
N. Gozlan, C. Roberto, P.-M. Samson, and P. Tetali · 2014
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F. Cavaletti and A. Mondino · 2015
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F. Cavaletti and A. Mondino · 2015
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Entropic Ricci curvature bounds for discrete interacting systems
M. Fathi and J. Maas · 2016
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Discrete curvature and abelian groups
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