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Asymptotic entropy of transformed random walks

Published online by Cambridge University Press:  28 January 2016

BEHRANG FORGHANI
BEHRANG FORGHANI*
Affiliation:
Department of Mathematics, University of Ottawa, Canada email behrang.forghani@uconn.edu
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Abstract

We consider general transformations of random walks on groups determined by Markov stopping times and prove that the asymptotic entropy (respectively, rate of escape) of the transformed random walks is equal to the asymptotic entropy (respectively, 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 formula from ergodic theory; its particular cases were established earlier by Kaimanovich [Differential entropy of the boundary of a random walk on a group. Uspekhi Mat. Nauk38(5(233)) (1983), 187–188] and Hartman et al [An Abramov formula for stationary spaces of discrete groups. Ergod. Th. & Dynam. Sys.34(3) (2014), 837–853].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1480 - 1491
Copyright
© Cambridge University Press, 2016 

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