Some probabilistic aspects of Yang-Mills

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Abstract/Contents

Abstract: This thesis develops some of the mathematical aspects of Yang-Mills theories, primarily in the setting of probability theory. First, we analyze finite gauge group lattice gauge theories at weak coupling, and in this setting compute expectations of Wilson loop observables as well as show exponential decay of correlations for local observables. Then, we shift to working directly in the continuum and analyze the Yang-Mills heat flow with random distributional initial data. Finally, we construct a state space which should support the 3D Yang-Mills measure - for some progress towards this end, we then use the previous results on the Yang-Mills heat flow to make some partial progress towards constructing the 3D Yang-Mills measure as a probability measure on our state space.

Type of resource	text
Form	electronic resource; remote; computer; online resource
Extent	1 online resource.
Place	California
Place	[Stanford, California]
Publisher	[Stanford University]
Copyright date	2022; ©2022
Publication date	2022; 2022
Issuance	monographic
Language	English

Author	Cao, Sky
Degree supervisor	Chatterjee, Sourav
Thesis advisor	Chatterjee, Sourav
Thesis advisor	Dembo, Amir
Thesis advisor	Diaconis, Persi
Degree committee member	Dembo, Amir
Degree committee member	Diaconis, Persi
Associated with	Stanford University, Department of Statistics

Genre	Theses
Genre	Text

Statement of responsibility	Sky Cao.
Note	Submitted to the Department of Statistics.
Thesis	Thesis Ph.D. Stanford University 2022.
Location	https://purl.stanford.edu/vv623vd2096

License: This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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