Flexibility of statistical properties for smooth systems satisfying the central limit theorem

2020/06/03 by Dolgopyat, Dmitry, Dong, Changguang, Kanigowski, Adam +1 · 4 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.02191

Abstract

In this paper we exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: (1) zero entropy; (2) weak but not strong mixing; (3) (polynomially) mixing but not K; (4) K but not Bernoulli; (5) non Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index 1.

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