Leading Order Asymptotics of a Multi-Matrix Partition Function for Colored Triangulations

Persistent Link:
http://hdl.handle.net/10150/293410
Title:
Leading Order Asymptotics of a Multi-Matrix Partition Function for Colored Triangulations
Author:
Acosta Jaramillo, Enrique
Issue Date:
2013
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 study the leading order asymptotics of a Random Matrix theory partition function related to colored triangulations. This partition function comes from a three Hermitian matrix model that has been introduced in the physics literature. We provide a detailed and precise description of the combinatorial objects that the partition function counts that has not appeared previously in the literature. We also provide a general framework for studying the leading order asymptotics of an N dimensional integral that one encounters studying the partition function of colored triangulations. The results are obtained by generalizing well know results for integrals coming from Hermitian matrix models with only one matrix that give the leading order asymptiotics in terms of a finite dimensional variational problem. We apply these results to the partition function for colored triangulations to show that the minimizing density of the variational problem is unique, and agrees with the one proposed in the physics literature. This provides the first complete mathematically rigorous description of the leading order asymptotics of this matrix model for colored triangulations.
Type:
text; Electronic Dissertation
Keywords:
Enumeration; Maps; Triangulations; Mathematics; Asymptotics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
McLaughlin, Kenneth D. T-R.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleLeading Order Asymptotics of a Multi-Matrix Partition Function for Colored Triangulationsen_US
dc.creatorAcosta Jaramillo, Enriqueen_US
dc.contributor.authorAcosta Jaramillo, Enriqueen_US
dc.date.issued2013-
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 study the leading order asymptotics of a Random Matrix theory partition function related to colored triangulations. This partition function comes from a three Hermitian matrix model that has been introduced in the physics literature. We provide a detailed and precise description of the combinatorial objects that the partition function counts that has not appeared previously in the literature. We also provide a general framework for studying the leading order asymptotics of an N dimensional integral that one encounters studying the partition function of colored triangulations. The results are obtained by generalizing well know results for integrals coming from Hermitian matrix models with only one matrix that give the leading order asymptiotics in terms of a finite dimensional variational problem. We apply these results to the partition function for colored triangulations to show that the minimizing density of the variational problem is unique, and agrees with the one proposed in the physics literature. This provides the first complete mathematically rigorous description of the leading order asymptotics of this matrix model for colored triangulations.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectEnumerationen_US
dc.subjectMapsen_US
dc.subjectTriangulationsen_US
dc.subjectMathematicsen_US
dc.subjectAsymptoticsen_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.advisorMcLaughlin, Kenneth D. T-R.en_US
dc.contributor.committeememberErcolani, Nicholas M.en_US
dc.contributor.committeememberFlaschka, Hermannen_US
dc.contributor.committeememberKennedy, Thomas G.en_US
dc.contributor.committeememberMcLaughlin, Kenneth D. T-R.en_US
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