Geodesic
Fluctuations of ergodic averages for amenable group actions
Uri Gabor1
1Hebrew University of Jerusalem, Israel
Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 1041-1058

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DOI

We show that for any countable amenable group action, along certain Følner sequences (those that have for any c>1 a two-sided c-tempered tail), one has a universal estimate for the number of fluctuations in the ergodic averages of L∞ functions. This estimate gives exponential decay in the number of fluctuations. Any two-sided Følner sequence can be thinned out to satisfy the above property. In particular, any countable amenable group admits such a sequence. This extends results of S. Kalikow and B. Weiss [1] for Zd actions and of N. Moriakov [3] for actions of groups with polynomial growth.
DOI : 10.4171/ggd/622
Classification : 28-XX
Mots-clés : Ergodic theorems, upcrossing inequalities, amenable group actions

Uri Gabor  1

1 Hebrew University of Jerusalem, Israel 
Uri Gabor. Fluctuations of ergodic averages for amenable group actions. Groups, geometry, and dynamics, Tome 15 (2021) no. 3, pp. 1041-1058. doi: 10.4171/ggd/622
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     pages = {1041--1058},
     year = {2021},
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     number = {3},
     doi = {10.4171/ggd/622},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/622/}
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