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We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets.
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Ollivier, YannY. (2009). Ricci curvature of Markov chains on metric spaces. J. Funct. Anal. 256 810–864
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Chow, Shui-NeeS.-N., Huang, WenW., Li, YaoY. andZhou, HaominH. (2012). Fokker–Planck equations for a free energy functional or Markov process on a graph. Arch. Ration. Mech. Anal. 203 969–1008
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Erbar, MatthiasM. andMaas, JanJ. (2012). Ricci curvature of finite Markov chains via convexity of the entropy. Arch. Ration. Mech. Anal. 206 997–1038
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Dai Pra, PaoloP. andPosta, GustavoG. (2013). Entropy decay for interacting systems via the Bochner–Bakry–Émery approach. Electron. J. Probab. 18 52
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Gigli, NicolaN. andMaas, JanJ. (2013). Gromov–Hausdorff convergence of discrete transportation metrics. SIAM J. Math. Anal. 45 879–899
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Mielke, AlexanderA. (2013). Geodesic convexity of the relative entropy in reversible Markov chains. Calc. Var. Partial Differential Equations 48 1–31
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Cited alongside, same era.
Lin, YongY. andYau, Shing-TungS.-T. (2010). Ricci curvature and eigenvalue estimate on locally finite graphs. Math. Res. Lett. 17 343–356
2010
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Maas, JanJ. (2011). Gradient flows of the entropy for finite Markov chains. J. Funct. Anal. 261 2250–2292
2011
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Mielke, AlexanderA. (2011). A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems. Nonlinearity 24 1329–1346
2011
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2013
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Ollivier, YannY. (2013). A visual introduction to Riemannian curvatures and some discrete generalizations. In Analysis and Geometry of Metric Measure Spaces. CRM Proc. Lecture Notes 56 197–220. Amer. Math. Soc., Providence, RI
2013
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Erbar, MatthiasM. andMaas, JanJ. (2014). Gradient flow structures for discrete porous medium equations. Discrete Contin. Dyn. Syst. 34 1355–1374
2014
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Erbar, MatthiasM., Maas, JanJ. andTetali, P.P. (2015). Discrete Ricci curvature bounds for Bernoulli–Laplace and random transposition models. Annales Fac. Sci. Toulouse (6) 24 781–800
2015
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