Cutoffs for product chains

Guan-Yu Chen, Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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
Volume128
Issue number11
DOIs
StatePublished - 1 Nov 2018

Keywords

  • Cutoffs
  • Product chains
  • Total variation and Hellinger distances

Fingerprint Dive into the research topics of 'Cutoffs for product chains'. Together they form a unique fingerprint.

Cite this