Secret sharing on the Poisson-Furstenberg boundary I
Dynamical Systems
2024-06-04 v1 Probability
Abstract
Recently, Vadim Kaimanovich presented a particular example of a measure on a product of two standard lamplighter groups such that the Poisson boundary of the induced random walk is non-trivial, but the boundary on the marginals is trivial. This was surprising since such behavior is not possible for measures of finite entropy. As we show in this paper, this secret-sharing phenomenon is possible precisely for pairs of amenable groups with non-trivial ICC-factors.
Cite
@article{arxiv.2406.01580,
title = {Secret sharing on the Poisson-Furstenberg boundary I},
author = {Andrei Alpeev},
journal= {arXiv preprint arXiv:2406.01580},
year = {2024}
}
Comments
14 p