Loop Group Factorization, Lattice Systems and OPUC
Publisher
The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
In this dissertation, starting from Verblunsky correspondence, we study the representationof the Gaussian free field in terms of Verblunsky sequence. We then explore connections of Verblunsky theory with loop group factorization and certain 1D Ising models. Next, we provide a new one-parameter family of Verblunsky sequences with their associated measure. At the end, we show how to translate instances of Verblunsky correspondence into partition function calculations of Ising models.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics