Examples of measures with trivial left and non-trivial right random walk tail boundary
Probability
2024-05-07 v3 Dynamical Systems
Abstract
In early 80's Vadim Kaimanovich presented a construction of a non-degenerate measure, on the standard lamplighter group, that has a trivial left and non-trivial right random walk tail boundary. We show that examples of such kind are possible precisely for amenable groups that have non-trivial factors with infinite conjugacy classes property.
Cite
@article{arxiv.2105.11359,
title = {Examples of measures with trivial left and non-trivial right random walk tail boundary},
author = {Andrei Alpeev},
journal= {arXiv preprint arXiv:2105.11359},
year = {2024}
}
Comments
11 pages, improved presentation