Journal of Applied Probability

Realization of an ergodic Markov chain as a random walk subject to a synchronizing road coloring

Kouji Yano and Kenji Yasutomi

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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.

Article information

J. Appl. Probab., Volume 48, Number 3 (2011), 766-777.

First available in Project Euclid: 23 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 37A35: Entropy and other invariants, isomorphism, classification 05C81: Random walks on graphs 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

Markov chain random walk in a directed graph road coloring problem Tsirelson's equation coupling from the past


Yano, Kouji; Yasutomi, Kenji. Realization of an ergodic Markov chain as a random walk subject to a synchronizing road coloring. J. Appl. Probab. 48 (2011), no. 3, 766--777. doi:10.1239/jap/1316796913.

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