Random walks of infinite moment on free semigroups
Dynamical Systems
2019-08-13 v1 Group Theory
Probability
Abstract
We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy criteria. In particular, we introduce the notion of w-logarithmic moment, and we show that if a random walk on a free semigroup has either finite entropy or finite w-logarithmic moment for some word w, then the space of infinite words with the resulting hitting measure is the Poisson boundary.
Cite
@article{arxiv.1712.00860,
title = {Random walks of infinite moment on free semigroups},
author = {Behrang Forghani and Giulio Tiozzo},
journal= {arXiv preprint arXiv:1712.00860},
year = {2019}
}