Symmetric Birkhoff sums in infinite ergodic theory
Dynamical Systems
2021-04-15 v3 Probability
Abstract
We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity.
Keywords
Cite
@article{arxiv.1307.7490,
title = {Symmetric Birkhoff sums in infinite ergodic theory},
author = {Jon. Aaronson and Zemer Kosloff and Benjamin Weiss},
journal= {arXiv preprint arXiv:1307.7490},
year = {2021}
}