The L2-cutoff for reversible Markov processes

Guan-Yu Chen*, Laurent Saloff-Coste

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Scopus citations


We consider the problem of proving the existence of an L2-cutoff for families of ergodic Markov processes started from given initial distributions and associated with reversible (more, generally, normal) Markov semigroups. This includes classical examples such as families of finite reversible Markov chains and Brownian motion on compact Riemannian manifolds. We give conditions that are equivalent to the existence of an L2-cutoff and describe the L2-cutoff time in terms of the spectral decomposition. This is illustrated by several examples including the Ehrenfest process and the biased (p, q)-random walk on the non-negative integers, both started from an arbitrary point.

Original languageEnglish
Pages (from-to)2246-2315
Number of pages70
JournalJournal of Functional Analysis
Issue number7
StatePublished - 1 Apr 2010


  • L-cutoff
  • Markov semigroups
  • Normal operators

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