Fluctuations of ergodic averages for actions of groups of polynomial growth

Nikita Moriakov

Research output: Contribution to journalArticleScientificpeer-review

Abstract

It was shown by S. Kalikow and B.Weiss that, given a measure-preserving action of Zd on a probability space X and a nonnegative measurable function f on X, the probability that the sequence of ergodic averages 1/(2k + 1)d Σ gϵ[-k,...,k]d f(g - x) has at least n fluctuations across an interval (α β) can be bounded from above by c1cn 2 for some universal constants c1 ϵ R and c2 ϵ (0, 1), which depend only on d; α β. The purpose of this article is to generalize this result to measure-preserving actions of groups of polynomial growth. As the main tool we develop a generalization of the effective Vitali covering theorem to groups of polynomial growth.

Original languageEnglish
Pages (from-to)255-273
Number of pages19
JournalStudia Mathematica
Volume240
Issue number3
DOIs
Publication statusPublished - 2018

Keywords

  • Fluctuations of ergodic averages
  • Groups of polynomial growth

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