Cutoffs for product chains

Guan-Yu Chen; Takashi Kumagai

doi:10.1016/j.spa.2018.01.002

Cutoffs for product chains

Guan-Yu Chen, Takashi Kumagai^*

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摘要

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.

原文	English
頁（從 - 到）	3840-3879
頁數	40
期刊	Stochastic Processes and their Applications
卷	128
發行號	11
DOIs	https://doi.org/10.1016/j.spa.2018.01.002
出版狀態	Published - 11月 2018

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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.",

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AB - 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.

KW - Cutoffs

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KW - Total variation and Hellinger distances

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JF - Stochastic Processes and their Applications

IS - 11

ER -

Cutoffs for product chains

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