A survey of Ricci curvature for metric spaces and Markov chains

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Li–Yau inequality on finite graphs via non-linear curvature dimension conditions (2014, unknown): “[17, 18, 19, 21]).”
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator (2011, background): “In the open Problem G in [22], Olliver asks for the possibility to relax this strong assumption.”
Curvature and transport inequalities for Markov chains in discrete spaces (2015, background): “The problem of proving a transport-entropy inequality for Markov chains with positive coarse Ricci curvature was raised in Problem J in [38].”
Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds (2017, methodology): “compatible with Lipschitz functions and Wasserstein metrics. Approaches in this direction have been made in [Bas81; Jou07; Jou09; Vey12]). However, the problem suggested by Ollivier (see Problem D in [Oll]), namely, if a lower curvature bound implies non-explosion (also known as stochastic completen”
Exponential ergodicity for Markov processes with random switching (2013, background): “ation (1.3) is not much of a restriction because we do not assume that ρ(i)>0. The best constant in this inequality is called the Wasserstein curvaturein [26, 27] and the coarse Ricci curvature in [29, 30], since it is heavily related to the geometry of the underlying space as illustrated in [34]”