Cutoff for product replacement on finite groups

Yuval Peres, Ryokichi Tanaka, Alex Zhai

Research output: Contribution to journalArticlepeer-review


We analyze a Markov chain, known as the product replacement chain, on the set of generating n-tuples of a fixed finite group G. We show that as n→ ∞, the total-variation mixing time of the chain has a cutoff at time 32nlogn with window of order n. This generalizes a result of Ben-Hamou and Peres (who established the result for G= Z/ 2) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is O(nlog n).

Original languageEnglish
Pages (from-to)823-853
Number of pages31
JournalProbability Theory and Related Fields
Issue number3-4
Publication statusPublished - 2020 Aug 1


  • Cutoff phenomenon
  • Markov chain
  • Mixing time
  • Product replacement algorithm

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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