Fluctuations of ergodic averages for amenable group actions

Uri Gabor

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arXiv · 1902.07912

Fluctuations of ergodic averages for amenable group actions

Uri Gabor

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Abstract

We show that for any countable amenable group action, along F{\o}lner 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 $L^{\infty}$ functions, and this estimate gives exponential decay in $n$. Any two-sided F{\o}lner 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 $\mathbb{Z}^{d}$ actions and of N. Moriakov for actions of groups with polynomial growth.

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BibTeX RIS

Uri Gabor. 2019-02-21. Fluctuations of ergodic averages for amenable group actions. https://arxiv.org/abs/1902.07912

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