Asymptotic entropy of transformed random walks

Abstract

We consider general transformations of random walks on groups determined by Markov stopping times and prove that 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, its particular cases were established earlier by Kaimanovich [1983] and Hartman, Lima, Tamuz [2014].

References in corpus (1)

• Asymptotic entropy and green speed for random walks on countable groups

Cited by in corpus (2)

• Random walks of infinite moment on free semigroups
• Isometric group actions with vanishing rate of escape on CAT(0) spaces