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Analogues of Amenability


Frisch, Joshua Robert (2021) Analogues of Amenability. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yymw-xd55.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Amenability: Group Theory: Dynamical Systems: Descriptive Set Theory
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2021. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2019.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Tamuz, Omer (co-advisor)
  • Kechris, Alexander S. (co-advisor)
Thesis Committee:
  • Katz, Nets H. (chair)
  • Vidnyánszky, Zoltán
  • Tamuz, Omer
  • Kechris, Alexander S.
Defense Date:5 May 2021
Record Number:CaltechTHESIS:05302021-185858708
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 3 adapted for ch. 5 adapted for ch. 4
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14206
Deposited By: Joshua Frisch
Deposited On:10 Jun 2021 15:39
Last Modified:03 Nov 2021 19:46

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