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Dimer Models and Local Systems
Dimer Models and Local Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151025
- ISBN
- 9798383566022
- DDC
- 510
- 저자명
- Shi, Haolin.
- 서명/저자
- Dimer Models and Local Systems
- 발행사항
- [Sl] : Yale University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 175 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
- 주기사항
- Advisor: Kenyon, Richard.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2024.
- 초록/해제
- 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.
- 일반주제명
- Mathematics
- 일반주제명
- Statistical physics
- 키워드
- Dimer models
- 키워드
- Web traces
- 기타저자
- Yale University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■007cr#unu||||||||
■020 ▼a9798383566022
■035 ▼a(MiAaPQ)AAI30996773
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aShi, Haolin.
■24510▼aDimer Models and Local Systems
■260 ▼a[Sl]▼bYale University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a175 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-02, Section: B.
■500 ▼aAdvisor: Kenyon, Richard.
■5021 ▼aThesis (Ph.D.)--Yale University, 2024.
■520 ▼aIn 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.
■590 ▼aSchool code: 0265.
■650 4▼aMathematics
■650 4▼aStatistical physics
■653 ▼aGeometric settings
■653 ▼aStatistical mechanics
■653 ▼aDimer models
■653 ▼aGraph connections
■653 ▼aWeb traces
■690 ▼a0405
■690 ▼a0217
■71020▼aYale University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-02B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160469▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
