Fluctuations of ergodic averages for amenable group actions

2019/02/21 by Gabor, Uri
#28D05 #28D15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.07912

Abstract

We show that for any countable amenable group action, along Følner sequences that have for any c>1 a two sided c-tempered tail, one have universal estimate for the probability that there are n fluctuations in the ergodic averages of L^∞ functions, and this estimate gives exponential decay in n. Any two-sided Følner sequence can be thinned out to satisfy the above property, and in particular, any countable amenble group admits such a sequence. This extends results of S. Kalikow and B. Weiss for ℤ^d actions and of N. Moriakov for actions of groups with polynomial growth.

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