Realization of finite-state mixing Markov chain as a random walk subject to a synchronizing road coloring

Kouji Yano; Kenji Yasutomi

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arXiv · 1006.0534

Realization of finite-state mixing Markov chain as a random walk subject to a synchronizing road coloring

Kouji Yano·Kenji Yasutomi

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Abstract

A mixing Markov chain is proved to be realized as a random walk in a directed graph subject to a synchronizing road coloring. The result ensures existence of appropriate random mappings in Propp--Wilson's coupling from the past. The proof is based on the road coloring theorem. A necessary and sufficient condition for approximate preservation of entropies is also given.

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Kouji Yano, Kenji Yasutomi. 2010-08-28. Realization of finite-state mixing Markov chain as a random walk subject to a synchronizing road coloring. https://arxiv.org/abs/1006.0534

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