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Realization of an Ergodic Markov Chain as a Random Walk Subject to a Synchronizing Road Coloring

Part of: Graph theory Markov processes Ergodic theory Random dynamical systems

Published online by Cambridge University Press:  14 July 2016

Kouji Yano  and
Kenji Yasutomi
Kouji Yano*
Affiliation:
Kobe University
Kenji Yasutomi*
Affiliation:
Ritsumeikan University
*
∗ Current address: Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan. Email address: kyano@math.kyoto-u.ac.jp
∗∗ Postal address: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577, Japan.
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Abstract

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An ergodic Markov chain is proved to be the realization of a random walk in a directed graph subject to a synchronizing road coloring. The result ensures the 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.

Keywords

Markov chainrandom walk in a directed graphroad coloring problemTsirelson's equationcoupling from the past

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 37A35: Entropy and other invariants, isomorphism, classification 05C81: Random walks on graphs 37H10: Generation, random and stochastic difference and differential equations
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 766 - 777
Copyright
Copyright © Applied Probability Trust 2011 

Footnotes

Research supported by KAKENHI (20740060).

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