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arXiv · 1404.0645

Moment bounds and concentration inequalities for slowly mixing dynamical systems

Sébastien Gouëzel·Ian Melbourne
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Abstract

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with nonstandard scaling $(n\log n)^{1/2}$.

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Sébastien Gouëzel, Ian Melbourne. 2014-04-02. Moment bounds and concentration inequalities for slowly mixing dynamical systems. https://arxiv.org/abs/1404.0645

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