Erdös-Rényi laws for dynamical systems

Manfred Denker, Matthew Nicol

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We establish Erdös-Rényi limit laws for Lipschitz observations on a class of non-uniformly expanding dynamical systems, including logistic-like maps. These limit laws give the maximal average of a time series over a time window of logarithmic length. We also give results on maximal averages of a time series arising from Hölder observations on intermittent-type maps over a time window of polynomial length. We consider the rate of convergence in the limit law for subshifts of finite type and establish a one-sided rate bound for Gibbs-Markov maps.

Original languageEnglish (US)
Pages (from-to)497-508
Number of pages12
JournalJournal of the London Mathematical Society
Volume87
Issue number2
DOIs
StatePublished - Apr 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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