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Moment bounds and concentration inequalities for slowly mixing dynamical systems. (English) Zbl 1351.37041

Summary: 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 \((n\log n)^{1/2}\).

MSC:

37A50 Dynamical systems and their relations with probability theory and stochastic processes
37A25 Ergodicity, mixing, rates of mixing
60F15 Strong limit theorems
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