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math.PR2016★ 11 cited
Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations
Ronen Eldan
We prove structure theorems for measures on the discrete cube and on Gaussian space, which provide sufficient conditions for mean-field behavior. These conditions rely on a new not…
math.PR2016
Transport-entropy inequalities and curvature in discrete-space Markov chains
Ronen Eldan, James R. Lee, Joseph Lehec
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. P…