Modified log-Sobolev inequalities for strongly log-concave distributions

2019/03/14 by Cryan, Mary, Guo, Heng, Mousa, Giorgos · 3 citations
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1903.06081

Abstract

We show that the modified log-Sobolev constant for a natural Markov chain which converges to an r-homogeneous strongly log-concave distribution is at least 1/r. Applications include a sharp mixing time bound for the bases-exchange walk for matroids, and a concentration bound for Lipschitz functions over these distributions.

Cited by

• Estimating Ising Models in Total Variation Distance
• Kac's Program and Relative Entropy Decay for Nonlinear Spin-Exchange Dynamics
• Curvature of basis exchange walks

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