Transport-entropy inequalities and curvature in discrete-space Markov chains

2016/04/23 by Eldan, Ronen, Lee, James R., Lehec, Joseph
#FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1604.06859

Abstract

We show that if the random walk on a graph has positive coarse Ricci curvature in the sense of Ollivier, then the stationary measure satisfies a W¹ transport-entropy inequality. Peres and Tetali have conjectured a stronger consequence, that a modified log-Sobolev inequality (MLSI) should hold, in analogy with the setting of Markov diffusions. We discuss how our entropy interpolation approach suggests a natural attack on the MLSI conjecture.

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