Computing Poisson Boundaries without Moment Conditions

The Poisson boundary is a measure theoretic object which classifies both the space of possible asymptotic events of a random walk and the space of bounded harmonic functions. For most identifications so far a moment condition has proved crucial. I will talk about joint works with Kunal Chawla, Behrang Forghani, Giullio Tiozzo and with Eduardo Silva where we show that, for the most part, these moment conditions are unnecessary. In particular I will talk about the classes of acylindrically hyperbolic groups and wreath products.