Lifting Markov chains to speed up mixing

Fang Chen, L. Lovász, Igor Pak

Research output: Chapter in Book/Report/Conference proceedingChapter

53 Citations (Scopus)

Abstract

There are several examples where the mixing time of a Markov chain can be reduced substantially, often to about its square root, by `lifting', i.e., by splitting each state into several states. In several examples of random walks on groups, the lifted chain not only mixes better, but is easier to analyze. We characterize the best mixing time achievable through lifting in terms of multicommodity flows. We show that the reduction to square root is best possible. If the lifted chain is time-reversible, then the gain is smaller, at most a factor of log(1/π0), where π0 is the smallest stationary probability of any state. We give an example showing that a gain of a factor of log(1/π0)/log log(1/π0) is possible.

Original languageEnglish
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
PublisherACM
Pages275-281
Number of pages7
Publication statusPublished - 1999
EventProceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99 - Atlanta, GA, USA
Duration: May 1 1999May 4 1999

Other

OtherProceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99
CityAtlanta, GA, USA
Period5/1/995/4/99

Fingerprint

Markov processes

ASJC Scopus subject areas

  • Software

Cite this

Chen, F., Lovász, L., & Pak, I. (1999). Lifting Markov chains to speed up mixing. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 275-281). ACM.

Lifting Markov chains to speed up mixing. / Chen, Fang; Lovász, L.; Pak, Igor.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, 1999. p. 275-281.

Research output: Chapter in Book/Report/Conference proceedingChapter

Chen, F, Lovász, L & Pak, I 1999, Lifting Markov chains to speed up mixing. in Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, pp. 275-281, Proceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99, Atlanta, GA, USA, 5/1/99.
Chen F, Lovász L, Pak I. Lifting Markov chains to speed up mixing. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM. 1999. p. 275-281
Chen, Fang ; Lovász, L. ; Pak, Igor. / Lifting Markov chains to speed up mixing. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. ACM, 1999. pp. 275-281
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