Abramov’s formula for random walks on groups.

Given a random walk on a countable group, any 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. These results are partially joint work with V. Kaimanovich.