### 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/π_{0}), where π_{0} is the smallest stationary probability of any state. We give an example showing that a gain of a factor of log(1/π_{0})/log log(1/π_{0}) is possible.

Original language | English |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Publisher | ACM |

Pages | 275-281 |

Number of pages | 7 |

Publication status | Published - 1999 |

Event | Proceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99 - Atlanta, GA, USA Duration: May 1 1999 → May 4 1999 |

### Other

Other | Proceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99 |
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City | Atlanta, GA, USA |

Period | 5/1/99 → 5/4/99 |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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.

}

TY - CHAP

T1 - Lifting Markov chains to speed up mixing

AU - Chen, Fang

AU - Lovász, L.

AU - Pak, Igor

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032673977&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0032673977

SP - 275

EP - 281

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

PB - ACM

ER -