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Fall 2015 A random pointwise ergodic theorem with Hardy field weights
Ben Krause, Pavel Zorin-Kranich
Illinois J. Math. 59(3): 663-674 (Fall 2015). DOI: 10.1215/ijm/1475266402

Abstract

Let $a_{n}$ be the random increasing sequence of natural numbers which takes each value independently with probability $n^{-a}$, $0<a<1/2$, and let $p(n)=n^{1+\varepsilon}$, $0<\varepsilon<1$. We prove that, almost surely, for every measure-preserving system $(X,T)$ and every $f\in L^{1}(X)$ the modulated, random averages

\[\frac{1}{N}\sum_{n=1}^{N}e(p(n))T^{a_{n}(\omega)}f\] converge to 0 pointwise almost everywhere.

Citation

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Ben Krause. Pavel Zorin-Kranich. "A random pointwise ergodic theorem with Hardy field weights." Illinois J. Math. 59 (3) 663 - 674, Fall 2015. https://doi.org/10.1215/ijm/1475266402

Information

Received: 12 January 2015; Revised: 24 March 2016; Published: Fall 2015
First available in Project Euclid: 30 September 2016

zbMATH: 1366.37012
MathSciNet: MR3554227
Digital Object Identifier: 10.1215/ijm/1475266402

Subjects:
Primary: 37A30

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

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Vol.59 • No. 3 • Fall 2015
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