Mixing times for uniformly ergodic Markov chains

David Aldous, László Lovász, Peter Winkler

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Consider the class of discrete time, general state space Markov chains which satisfy a "uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting equivalence (up to universal constants) of different quantifications of mixing time. This work combines three areas of Markov theory which are rarely connected: the potential-theoretical characterization of optimal stopping times, the theory of stability and convergence to stationarity for general-state chains, and the theory surrounding mixing times for finite-state chains.

Original languageEnglish
Pages (from-to)165-185
Number of pages21
JournalStochastic Processes and their Applications
Volume71
Issue number2
DOIs
Publication statusPublished - Nov 15 1997

Keywords

  • Markov chain
  • Minorization
  • Mixing time
  • Randomized algorithm
  • Stopping time

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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