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Thursday, February 06, 2025
4:00 PM - 5:00 PM

LA Probability Forum

The Poisson boundary of hyperbolic groups without moment conditions
Kunal Chawla, Department of Mathematics, Princeton University,

USC Kaprielian (KAP) 414

Given a random walk on a countable group, the Poisson boundary is a measure space which captures all asymptotic events of the markov chain. The Poisson boundary can sometimes be identified with a concrete geometric boundary, but almost all previous results relied strongly on moment conditions of the random walk. I will discuss a technique which allows us to identify the Poisson boundary on any group with hyperbolic properties without moment conditions, new even in the free group case, making progress on a question of Kaimanovich and Vershik. This is joint work with Behrang Forghani, Joshua Frisch, and Giulio Tiozzo.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at mathinfo@caltech.edu.