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We establish three remarkable consequences of non-negative curvature for sparse Markov chains.
Random Cayley graphs and expanders
Noga Alon and Yuval Roichman · 1994
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Persi Diaconis · 1996
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Florentin Münch · 2019
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Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds
Florentin Münch and Radosław K Wojciechowski · 2019
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Marzieh Eidi and Jürgen Jost · 2020
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Geometric and spectral properties of directed graphs under a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, and Taiki Yamada · 2020
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Taiki Yamada · 2016
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J. Jost · 2017
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David A. Levin and Yuval Peres · 2017
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Cutoff for conjugacy-invariant random walks on the permutation group
Nathanaël Berestycki and BatıŞengül · 2019
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Yann Ollivier
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Jürgen Jost and Florentin Münch · 2021
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Cutoff for non-negatively curved Markov chains
Justin Salez · 2021
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Sparse expanders have negative curvature
Justin Salez · 2021
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A finitary structure theorem for vertex-transitive graphs of polynomial growth
Romain Tessera and Matthew C. H. Tointon · 2021
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Heat flow and concentration of measure on directed graphs with a lower Ricci curvature bound
Ryunosuke Ozawa, Yohei Sakurai, and Taiki Yamada · 2022
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