자료유형  

 학위논문

Control Number  

0017160469

International Standard Book Number  

9798383566022

Dewey Decimal Classification Number  

510

Main Entry-Personal Name  

Shi, Haolin.

Publication, Distribution, etc. (Imprint  

[S.l.] : Yale University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

175 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-02, Section: B.

General Note  

Advisor: Kenyon, Richard.

Dissertation Note  

Thesis (Ph.D.)--Yale University, 2024.

Summary, Etc.  

요약In this thesis we study several generalizations of the dimer model to higher rank geometric settings. The dimer models, first studied as a toy model in statistical mechanics, exhibit beautiful mathematical structures. It can be exactly enumerated and its probabilistic properties can be studied algebraically. It is also related to geometry and topology.Many versions and generalizations of the dimer model have been studied. Some examples are double dimer models on surfaces. We generalize double dimer models to n-dimer models and prove a generalization of Kasteleyn's theorem. Boundaried double dimer models have been extensively studied on the disk. We generalize such results to the annulus. Finally, we study boundaried triple dimer models on the disk and explicitly compute probabilities of triple dimer models on the upper half plane in the scaling limit.

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Statistical physics.

Index Term-Uncontrolled  

Geometric settings

Index Term-Uncontrolled  

Statistical mechanics

Index Term-Uncontrolled  

Dimer models

Index Term-Uncontrolled  

Graph connections

Index Term-Uncontrolled  

Web traces

Added Entry-Corporate Name  

Yale University Mathematics

Host Item Entry  

Dissertations Abstracts International. 86-02B.

Electronic Location and Access  

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Control Number  

joongbu:657363