Exponential return times in a zero-entropy process

2011/01/10 by Paulina Grzegorek, Grzegorek, Paulina, Michal Kupsa +1
Mathematics · Medicine · #37A05 #37A25 #60G10 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1101.1828

openalex publication_date 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a zero-entropy weakly mixing finite-valued process with the exponential limit law for return resp. hitting times. This limit law is obtained in almost every point, taking the limit along the full sequence of cylinders around the point. Till now, the exponential limit law for return resp. hitting times, taking the limit along the full sequence of cylinders, have been obtained only in positive-entropy processes satisfying some strong mixing conditions of Rossenblatt type.

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