Products of random walks on finite groups with moderate growth

Guan-Yu Chen, Takashi Kumagai

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we consider products of random walks on finite groups with moderate growth and discuss their cutoffs in the total variation. Based on several comparison techniques, we are able to identify the total variation cutoff of discrete time lazy random walks with the Hellinger distance cutoff of continuous time random walks. Along with the cutoff criterion for Laplace transforms, we derive a series of equivalent conditions on the existence of cutoffs, including the existence of pre-cutoffs, Peres' product condition and a formula generated by the graph diameters. For illustration, we consider products of Heisenberg groups and randomized products of finite cycles.

Original languageEnglish
Pages (from-to)281-302
Number of pages22
JournalTohoku Mathematical Journal
Volume71
Issue number2
DOIs
StatePublished - 1 Jun 2019

Keywords

  • Moderate growth
  • Product chains
  • Random walks

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