The mixing time for simple exclusion

• 成果类型: Article
• 署名作者: Morris, Ben
• 署名单位: University of California System; University of California Davis
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000728
• 发表日期: 2006
• 页码: 615-635
• 关键词: logarithmic sobolev inequality; spectral gap; kawasaki; DYNAMICS

摘要

We obtain a tight bound of O(L(2)logk) for the mixing time of the exclusion process in Z(d)/LZ(d) with k <= (1)/L-2(d) particles. Previously the best bound. based oil the log Sobolev constant determined by Yau was not tight for small k. When dependence on the dimension d is considered. our bounds are all improvement for all k. We also get bounds for the relaxation time that are lower Order in d than previous estimates: our bound of O(L-2 log d) improves oil the earlier bound O(L(2)d) obtained by Quastel. Our proof is based oil all auxiliary Markov chain we call the chameleon process, which may be of independent interest.