Abstract
We discuss universal estimates for the probability that there are many fluctuations in the ergodic averages of $L^{1}$ functions. Our methods involve an effective Vitali covering type of theorem and are valid for $\mathbb{Z}^{d}$ actions, for any $d \in \mathbb{N}$. For nonnegative functions we get an exponential decay for the probability of a large number of fluctuations.
Citation
Steven Kalikow. Benjamin Weiss. "Fluctuations of ergodic averages." Illinois J. Math. 43 (3) 480 - 488, Fall 1999. https://doi.org/10.1215/ijm/1255985104
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