Growth of normalizing sequences in limit theorems for conservative maps
Dynamical Systems
2018-04-02 v1
Abstract
We consider normalizing sequences that can give rise to nondegenerate limittheorems for Birkhoff sums under the iteration of a conservative map. Mostclassical limit theorems involve normalizing sequences that are polynomial,possibly with an additional slowly varying factor. We show that, ingeneral, there can be no nondegenerate limit theorem with a normalizingsequence that grows exponentially, but that there are examples where itgrows like a stretched exponential, with an exponent arbitrarily close to 1.
Cite
@article{arxiv.1803.11472,
title = {Growth of normalizing sequences in limit theorems for conservative maps},
author = {Sébastien Gouëzel},
journal= {arXiv preprint arXiv:1803.11472},
year = {2018}
}