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Is it possible to construct a Markov chain with two (and only two) distinct invariant distributions?

Is it possible to construct a Markov chain with two (and only two) distinct invariant distributions?

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Answer #1

other way to understand :

The set of invariant distributions is a convex set. If it is not a unique, it contains the line segment connecting any two distinct invariant distributions. So its cardinality cannot be a finite number greater than 1. Either it's unique or there are infinitely many of them.  

if you have still doubts please ask ! thank you :))

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