Cutoffs for product chains

Guan-Yu Chen; Takashi Kumagai

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arXiv · 1701.06665

Cutoffs for product chains

Guan-Yu Chen·Takashi Kumagai

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Abstract

In this article, we consider products of ergodic Markov chains and discuss their cutoffs in the total variation. Through a new inequality relating the total variation and the Hellinger distance, we may identify the total variation cutoffs with cutoffs in the Hellinger distance. This provides a new scheme to study the total variation mixing of Markov chains, in particular, product chains. In the theoretical framework, a series of criteria are introduced to examine cutoffs and a comparison of mixing between the product chain and its coordinate chains is made in detail. For illustration, we consider products of two-state chains, cycles and other typical examples.

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Guan-Yu Chen, Takashi Kumagai. 2017-02-09. Cutoffs for product chains. https://arxiv.org/abs/1701.06665

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