Random Walks and the Regeneration Time

Andrew Beveridge, László Lovász

Research output: Contribution to journalArticle

2 Citations (Scopus)


Consider a graph G and a random walk on it. We want to stop the random walk at certain times (using an optimal stopping rule) to obtain independent samples from a given distribution ρ on the nodes. For an undirected graph, the expected time between consecutive samples is maximized by a distribution equally divided between two nodes, and so the worst expected time is 1/4 of the maximum commute time between two nodes. In the directed case, the expected time for this distribution is within a factor of 2 of the maximum.

Original languageEnglish
Pages (from-to)57-62
Number of pages6
JournalJournal of Graph Theory
Issue number2
Publication statusPublished - Oct 1998


  • Commute time
  • Random walk

ASJC Scopus subject areas

  • Geometry and Topology

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