Transport-entropy inequalities and curvature in discrete-space Markov chains
Probability
2016-12-28 v2 Metric Geometry
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 W^1 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.
Keywords
Cite
@article{arxiv.1604.06859,
title = {Transport-entropy inequalities and curvature in discrete-space Markov chains},
author = {Ronen Eldan and James R. Lee and Joseph Lehec},
journal= {arXiv preprint arXiv:1604.06859},
year = {2016}
}
Comments
To appear in "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek"