MODIFIED LOG-SOBOLEV INEQUALITIES FOR STRONGLY LOG-CONCAVE DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Cryan, Mary; Guo, Heng; Mousa, Giorgos
• 署名单位: University of Edinburgh
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1453
• 发表日期: 2021
• 页码: 506-525
• 关键词: mixing time-bounds; algorithm; models

摘要

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.