Erd\H{o}s-R\'enyi laws for exponentially and polynomially mixing dynamical systems

Erdős-Rényi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdős-Rényi type limit laws for Hölder observables on dynamical systems modeled by Young Towers with exponential and polynomial tails. This exten...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-08, Vol.151 (8), p.3415
Hauptverfasser: Nicolai Haydn, Matthew Nicol
Format: Artikel
Sprache:eng
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Zusammenfassung:Erdős-Rényi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdős-Rényi type limit laws for Hölder observables on dynamical systems modeled by Young Towers with exponential and polynomial tails. This extends earlier results on Erdős-Rényi limit laws to a broad class of dynamical systems with some degree of hyperbolicity.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/16091