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

@inproceedings{Yano2010RealizationOF,
  title={Realization of finite-state mixing Markov chain as a random walk subject to a synchronizing road coloring},
  author={Kouji Yano and Kenji Yasutomi},
  year={2010}
}
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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