Question: Suppose a time-reversible Markov chain has transition matrix P and stationary distribution . Show that the Markov chain can be regarded as a random walk

Suppose a time-reversible Markov chain has transition matrix P and stationary distribution π. Show that the Markov chain can be regarded as a random walk on a weighted graph with edge weights w(i, j) = π_iT_ij for all states i and j.

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