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. https://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:

https://resolver.caltech.edu/CaltechTHESIS:05262017-150152046

DOI:

10.7907/Z9R49NTF

Related URLs:

URL	URL Type	Description
http://arxiv.org/abs/1608.01331	arXiv	Article adapted for Chapter 1.
http://arxiv.org/abs/1501.04079	arXiv	Article adapted for Chapter 2.
http://arxiv.org/abs/1501.04373	arXiv	Article adapted for Chapter 3.
http://arxiv.org/abs/1603.05013	arXiv	Article adapted for Chapter 4.
http://arxiv.org/abs/1503.06360	arXiv	Article adapted for Chapter 5.
http://arxiv.org/abs/1603.09026	arXiv	Article adapted for Chapter 6.

ORCID:

Author	ORCID
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:

04 Oct 2019 00:16

Thesis Files

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