A Poisson limit theorem for Gibbs-Markov maps
Dynamical Systems
2021-04-08 v1
Abstract
We prove for Gibbs-Markov maps that the number of visits to a sequence of shrinking sets with bounded cylindrical lengths converges in distribution to a Poisson law. Applying to continued fractions, this result extends Doeblin's Poisson limit theorem.
Keywords
Cite
@article{arxiv.2010.14365,
title = {A Poisson limit theorem for Gibbs-Markov maps},
author = {Xuan Zhang},
journal= {arXiv preprint arXiv:2010.14365},
year = {2021}
}