Cutoffs for product chains
Probability
2017-02-13 v2
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.
Keywords
Cite
@article{arxiv.1701.06665,
title = {Cutoffs for product chains},
author = {Guan-Yu Chen and Takashi Kumagai},
journal= {arXiv preprint arXiv:1701.06665},
year = {2017}
}