The Poisson boundary of discrete subgroups of semisimple Lie groups without moment conditions
Kunal Chawla, Behrang Forghani, Joshua Frisch, Giulio Tiozzo
Published: 2025/9/2
Abstract
We show that the Poisson boundary of random walks of finite entropy on Zariski-dense discrete subgroups of semisimple Lie groups equals the Furstenberg boundary of the corresponding symmetric spaces equipped with the hitting measure, without assuming any moment condition on the random walk.