Erdos-Renyi 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 extends earlier results on Erdős-Rényi limit laws to a broad class of dynamical systems with some degree of hyperbolicity.

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