Cutoffs for product chains

Guan-Yu Chen, Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider products of ergodic Markov chains and discuss their cutoffs in total variation. Our framework is general in that rates to pick up coordinates are not necessary equal, and different coordinates may correspond to distinct chains. We give necessary and sufficient conditions for cutoffs of product chains in terms of those of coordinate chains under certain conditions. A comparison of mixing times between the product chain and its coordinate chains is made in detail as well. Examples are given to show that neither cutoffs for product chains nor for coordinate chains imply others in general.

Original languageEnglish
Pages (from-to)3840-3879
Number of pages40
JournalStochastic Processes and their Applications
Issue number11
StatePublished - 1 Nov 2018


  • Cutoffs
  • Product chains
  • Total variation and Hellinger distances

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