Arcsine and Darling--Kac laws for piecewise linear random interval maps
Dynamical Systems
2022-09-23 v3 Probability
Abstract
We give examples of piecewise linear random interval maps satisfying arcsine and Darling--Kac laws, which are analogous to Thaler's arcsine and Aaronson's Darling--Kac laws for the Boole transform. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.
Cite
@article{arxiv.2108.01332,
title = {Arcsine and Darling--Kac laws for piecewise linear random interval maps},
author = {Genji Hata and Kouji Yano},
journal= {arXiv preprint arXiv:2108.01332},
year = {2022}
}