Probabilistic Laws on Infinite Groups
Group Theory
2023-04-19 v1 Probability
Abstract
We study the probability that certain laws are satisfied on infinite groups, focusing on elements sampled by random walks. For several group laws, including the metabelian one, we construct examples of infinite groups for which the law holds with high probability, but the group does not satisfy the law virtually. On the other hand, we show that if an infinite group satisfies the law with positive probability, then it is virtually abelian.
Keywords
Cite
@article{arxiv.2304.09144,
title = {Probabilistic Laws on Infinite Groups},
author = {Gideon Amir and Guy Blachar and Maria Gerasimova and Gady Kozma},
journal= {arXiv preprint arXiv:2304.09144},
year = {2023}
}
Comments
39 pages,1 figure