Analogues of Amenability

Author: Frisch, Joshua Robert

Year: 2021

Degree: Dissertation (Ph.D.)

Advisors: Tamuz, Omer; Kechris, Alexander S.

Committee Members: Katz, Nets H.; Vidnyánszky, Zoltán; Tamuz, Omer; Kechris, Alexander S.

Option: Mathematics

DOI: 10.7907/yymw-xd55

Abstract

In this thesis I study multiple notions related to and inspired by amenability coming from the points of the view of random walks on groups, dynamical systems, Borel equivalence relations, and descriptive linear algebra. In particular I study notions related to harmonic functions, invariant measures, hyperfiniteness, and dichotomy theorems.

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