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

Dmitry Dolgopyat, Changguang Dong, Adam Kanigowski, Peter Nándori

Published 2020-06-03Version 1

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 $1$.