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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 7, 2024

10:00 AM

APM 7218

Research Areas

Algebra Ergodic Theory and Dynamical Systems Probability Theory

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