FLUCTUATIONS OF ERGODIC AVERAGES

Steven Kalikow; Benjamin Weiss

doi:10.1215/ijm/1255985104

FLUCTUATIONS OF ERGODIC AVERAGES

Steven Kalikow
, Benjamin Weiss

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We discuss universal estimates for the probability that there are many fluctuations in the ergodic averages of L¹ functions. Our methods involve an effective Vitali covering type of theorem and are valid for Z^d actions, for any d∈N. For nonnegative functions we get an exponential decay for the probability of a large number of fluctuations.

Original language	English
Pages (from-to)	480-488
Number of pages	9
Journal	Illinois Journal of Mathematics
Volume	43
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1255985104
State	Published - 1 Sep 1999

Bibliographical note

Publisher Copyright:
© 1999 University of Illinois at Urbana-Champaign.

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AB - We discuss universal estimates for the probability that there are many fluctuations in the ergodic averages of L1 functions. Our methods involve an effective Vitali covering type of theorem and are valid for Zd actions, for any d∈N. For nonnegative functions we get an exponential decay for the probability of a large number of fluctuations.

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FLUCTUATIONS OF ERGODIC AVERAGES

Abstract

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