Transformed Random Walks - Forghani, Behrang (Université d'Ottawa / University of Ottawa, 2015)
We consider transformations of a given random walk on a countable group determined by Markov stopping times. We prove that these transformations preserve the Poisson boundary. Moreover, under some mild conditions, the asymptotic entropy (resp., rate of escape) of the transformed random walks is equal to the asymptotic entropy (resp., rate of escape) of the original random walk multiplied by the expectation of the corresponding stopping time. This is an analogue of the well-known Abramov's formula from ergodic theory.
Keywords: Poisson boundary; Random walks on groups; Stopping times; Entropy; Drift