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January 2021 Modified log-Sobolev inequalities for strongly log-concave distributions
Mary Cryan, Heng Guo, Giorgos Mousa
Ann. Probab. 49(1): 506-525 (January 2021). DOI: 10.1214/20-AOP1453

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.

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Mary Cryan. Heng Guo. Giorgos Mousa. "Modified log-Sobolev inequalities for strongly log-concave distributions." Ann. Probab. 49 (1) 506 - 525, January 2021. https://doi.org/10.1214/20-AOP1453

Information

Received: 1 September 2019; Published: January 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.1214/20-AOP1453

Subjects:
Primary: 05B35, 60J10

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • January 2021
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