Convergence of Time-Inhomogeneous Random Walks on Finite Groups with Applications to Universality for Random Groups

Citation

Gorokhovsky, Elia Peter (2023) Convergence of Time-Inhomogeneous Random Walks on Finite Groups with Applications to Universality for Random Groups. Senior thesis (Major), California Institute of Technology. doi:10.7907/s4c4-hk39. https://resolver.caltech.edu/CaltechTHESIS:06112023-083707212

Abstract

We study time-inhomogeneous random walks on finite groups in the case where each random walk step need not be supported on a generating set of the group. When the supports of the random walk steps satisfy a natural condition involving normal subgroups of quotients of the group, we show that the random walk converges to the uniform distribution on the group, and give bounds for the convergence rate using spectral properties of the random walk steps. As applications, we prove a general universality theorem for quotients of the free group on n generators as n → ∞, and another universality theorem for cokernels of random integer matrices with dependent entries.

Thesis Files