CUTOFF PHENOMENON FOR THE ASYMMETRIC SIMPLE EXCLUSION PROCESS AND THE BIASED CARD SHUFFLING

• 成果类型: Article
• 署名作者: Labbe, Cyril; Lacoin, Hubert
• 署名单位: Universite PSL; Universite Paris-Dauphine; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1290
• 发表日期: 2019
• 页码: 1541-1586
• 关键词: conservation-laws; mixing times; CONVERGENCE; profile; limit

摘要

We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our results show that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic comparisons and concentration inequalities.