Flexibility of statistical properties for smooth systems satisfying the central limit theorem
Dynamical Systems
2020-06-17 v2
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 ; (4) 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 .
Cite
@article{arxiv.2006.02191,
title = {Flexibility of statistical properties for smooth systems satisfying the central limit theorem},
author = {Dmitry Dolgopyat and Changguang Dong and Adam Kanigowski and Peter Nándori},
journal= {arXiv preprint arXiv:2006.02191},
year = {2020}
}