Given a random walk on a countable group, any Markov stopping time gives
rise to a new random walk on the same group. We will show that the
asymptotic entropy (rate of escape) of such transformations are equal to
the asymptotic entropy (rate of escape) of the original random walk times
the expectation of the stopping time. This fact is an analogue of the
Abramov formula from ergodic theory. The proof is based on the fact that
the Poisson boundaries of these random walks are the same.
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Last modified: April 08 2016 - 20:30:35