Department of Mathematics,
University of California San Diego
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Math 211A - Algebra Seminar
Prof. Keivan Mallahi-Karai
Constructor University
A Central limit theorem for random walks on horospherical products of Gromov hyperbolic spaces
Abstract:
Let \(G\) be a countable group acting by isometries on a metric space \((M, d)\), and let \(\mu\) denote a probability measure on \(G\). The \(\mu\)-random walk on \(M\) is the random process defined by
\[Z_n=X_n \dots X_1 o,\]
where \(o \in M\) is a fixed base point, and \(X_i\) are independent \(\mu\)-distributed random variables.
Studying statistical properties of the displacement sequence \(D_n:= d(Z_n, o)\) has been a topic of current research.
In this talk, which is based on a joint work with Amin Bahmanian, Behrang Forghani, and Ilya Gekhtman, I will discuss a central limit theorem for \(D_n\) in the case that \(M\) is the horospherical product of Gromov hyperbolic spaces.
Host: Alireza Golsefidy
May 6, 2024
3:00 PM
APM 7321
Research Areas
Algebra Ergodic Theory and Dynamical Systems Probability Theory****************************
