Erdos-Renyi laws for exponentially and polynomially mixing dynamical systems

TL;DR

This paper extends Erdos-Renyi limit laws to a broad class of hyperbolic dynamical systems modeled by Young Towers, providing insights into the scale of fluctuations in time-averages for these systems.

Contribution

It establishes Erdos-Renyi type limit laws for Holder observables on Young Tower models with exponential and polynomial tails, broadening previous results.

Findings

Erdos-Renyi laws hold for systems with exponential tails.

Erdos-Renyi laws hold for systems with polynomial tails.

Results apply to a broad class of hyperbolic dynamical systems.

Abstract

Erdos-Renyi 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 Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by Young Towers with exponential and polynomial tails. This extends earlier results on Erdos-Renyi limit laws to a broad class of dynamical systems with some degree of hyperbolicity.