The asymptotic expansion of the partition function of random matrices

Persistent Link:
http://hdl.handle.net/10150/280566
Title:
The asymptotic expansion of the partition function of random matrices
Author:
Pierce, Virgil
Issue Date:
2004
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 or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We explore two methods for calculating the Taylor Coefficients of the terms of the asymptotic expansion of the partition function of random matrices for specific even potentials. The first of these methods applies to the leading order term. We show that this term has an elementary form in terms of a solution to an algebraic equation. This generates a general formula for the Taylor Coefficients of this term. Next we exploit the relationship between orthogonal polynomials and the Toda Lattice Equations to derive ODE's for the general terms of the expansion of the partition function of random matrices, which leads to a method of calculating the Taylor Coefficients of these functions.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Ercolani, Nicholas M.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleThe asymptotic expansion of the partition function of random matricesen_US
dc.creatorPierce, Virgilen_US
dc.contributor.authorPierce, Virgilen_US
dc.date.issued2004en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractWe explore two methods for calculating the Taylor Coefficients of the terms of the asymptotic expansion of the partition function of random matrices for specific even potentials. The first of these methods applies to the leading order term. We show that this term has an elementary form in terms of a solution to an algebraic equation. This generates a general formula for the Taylor Coefficients of this term. Next we exploit the relationship between orthogonal polynomials and the Toda Lattice Equations to derive ODE's for the general terms of the expansion of the partition function of random matrices, which leads to a method of calculating the Taylor Coefficients of these functions.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorErcolani, Nicholas M.en_US
dc.identifier.proquest3132249en_US
dc.identifier.bibrecord.b46709411en_US
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