Markov chain mixing time on cycles

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Gerencser, Balazs

关键词: Markov chain;    Mixing time;    Cycle;    Non-reversible;   

DOI  :  10.1016/j.spa.2011.07.007

来源: Elsevier

【 摘 要 】

Mixing time quantifies the convergence speed of a Markov chain to the stationary distribution. It is an important quantity related to the performance of MCMC sampling. It is known that the mixing time of a reversible chain can be significantly improved by lifting, resulting in an irreversible chain, while changing the topology of the chain. We supplement this result by showing that if the connectivity graph of a Markov chain is a cycle, then there is an Omega(n(2)) lower bound for the mixing time. This is the same order of magnitude that is known for reversible chains on the cycle. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free