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I would be curious to know if there's still open question about discrete markovian chains

Sasha Patotski
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LaurentOutang
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  • You might find some of the links at *[What are some open research problems in Stochastic Processes?](http://math.stackexchange.com/questions/321155/what-are-some-open-research-problems-in-stochastic-processes/406022#406022)*. – Gareth Oct 29 '13 at 10:31

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Chapter 23 of Markov Chains and Mixing Times by Levin, Peres, and Wilmer is called "Open Problems". The book is available online here.