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Approximation and Classification in the Ergodic Theory of Nonamenable Groups

Citation

Burton, Peter J. (2017) Approximation and Classification in the Ergodic Theory of Nonamenable Groups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9R49NTF. http://resolver.caltech.edu/CaltechTHESIS:05262017-150152046

Abstract

This thesis is a contribution to the theory of measurable actions of discrete groups on standard probability spaces. The focus is on nonamenable acting groups. It is organized into two parts. The first part deals with a notion called weak equivalence, which describes a sense in which such actions can approximate each other. The second part deals with the concept of entropy for measure preserving actions of sofic groups.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics, ergodic theory
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics: 2014, 2016.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Kechris, Alexander S. (chair)
  • Katz, Nets H.
  • Mantovan, Elena
  • Lupini, Martino
Defense Date:15 May 2017
Record Number:CaltechTHESIS:05262017-150152046
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05262017-150152046
DOI:10.7907/Z9R49NTF
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1608.01331arXivArticle adapted for Chapter 1.
http://arxiv.org/abs/1501.04079arXivArticle adapted for Chapter 2.
http://arxiv.org/abs/1501.04373arXivArticle adapted for Chapter 3.
http://arxiv.org/abs/1603.05013arXivArticle adapted for Chapter 4.
http://arxiv.org/abs/1503.06360arXivArticle adapted for Chapter 5.
http://arxiv.org/abs/1603.09026arXivArticle adapted for Chapter 6.
ORCID:
AuthorORCID
Burton, Peter J.0000-0002-0348-8385
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10213
Collection:CaltechTHESIS
Deposited By: Peter Burton
Deposited On:02 Jun 2017 20:15
Last Modified:16 Jun 2017 23:00

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