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Cutoffs for product chains

Author

Listed:
  • Chen, Guan-Yu
  • Kumagai, Takashi

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.

Suggested Citation

  • Chen, Guan-Yu & Kumagai, Takashi, 2018. "Cutoffs for product chains," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3840-3879.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3840-3879
    DOI: 10.1016/j.spa.2018.01.002
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    References listed on IDEAS

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    1. Barrera, Javiera & Lachaud, Béatrice & Ycart, Bernard, 2006. "Cut-off for n-tuples of exponentially converging processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1433-1446, October.
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