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


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.


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.

Item Type:Thesis (Senior thesis (Major))
Subject Keywords:Probability, group theory, random matrices, random walks
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Robert P. Balles Caltech Mathematics Scholar Award, 2023. Herbert J. Ryser Memorial Scholarship, 2021.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Tamuz, Omer
Thesis Committee:
  • Tamuz, Omer (chair)
  • Mazel-Gee, Aaron
  • Song, Antoine Y.
Defense Date:14 June 2023
Non-Caltech Author Email:eliapgorokhovsky (AT)
Funding AgencyGrant Number
Samuel P. and Frances Krown Summer Undergraduate Research FellowshipUNSPECIFIED
Record Number:CaltechTHESIS:06112023-083707212
Persistent URL:
Gorokhovsky, Elia Peter0000-0001-5901-9783
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16103
Deposited By: Elia Gorokhovsky
Deposited On:12 Jun 2023 18:37
Last Modified:16 Jun 2023 22:31

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