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Enumeration in Stochastic Processes and Polyhedral Geometry
Enumeration in Stochastic Processes and Polyhedral Geometry
Detailed Information
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103534
- ISBN
- 9798280710900
- DDC
- 510
- 저자명
- Jiang, Yuhan.
- 서명/저자
- Enumeration in Stochastic Processes and Polyhedral Geometry
- 발행사항
- [Sl] : Harvard University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 106 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Williams, Lauren K.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2025.
- 초록/해제
- 요약This dissertation explores the combinatorics of Markov chains and polyhedral geometry, with a focus on the asymmetric simple exclusion process (ASEP) and the Ehrhart theory of polytopes. The first part addresses the stationary distribution of stochastic models, including the open ASEP, the Arndt-Heinzel-Rittenberg (AHR) model and the doubly ASEP (DASEP). We give a two-layer simple random walk interpretation for the open ASEP model, a tableaux formula for the AHR model, and show that the DASEP exhibits homomesy phenomenon. The second part of the dissertation studies the Ehrhart theory of positroid polytopes and alcoved polytopes. We present combinatorial formulas for the h∗ -polynomials of positroid polytopes and alcoved polytopes. We also prove a connection between our shelling formula with decorated ordered set partitions.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Statistics
- 일반주제명
- Applied mathematics
- 키워드
- Ehrhart theory
- 키워드
- Markov chains
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798280710900
■035 ▼a(MiAaPQ)AAI32040331
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aJiang, Yuhan.▼0(orcid)0000-0002-2081-0727
■24510▼aEnumeration in Stochastic Processes and Polyhedral Geometry
■260 ▼a[Sl]▼bHarvard University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a106 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Williams, Lauren K.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2025.
■520 ▼aThis dissertation explores the combinatorics of Markov chains and polyhedral geometry, with a focus on the asymmetric simple exclusion process (ASEP) and the Ehrhart theory of polytopes. The first part addresses the stationary distribution of stochastic models, including the open ASEP, the Arndt-Heinzel-Rittenberg (AHR) model and the doubly ASEP (DASEP). We give a two-layer simple random walk interpretation for the open ASEP model, a tableaux formula for the AHR model, and show that the DASEP exhibits homomesy phenomenon. The second part of the dissertation studies the Ehrhart theory of positroid polytopes and alcoved polytopes. We present combinatorial formulas for the h∗ -polynomials of positroid polytopes and alcoved polytopes. We also prove a connection between our shelling formula with decorated ordered set partitions.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aStatistics
■650 4▼aApplied mathematics
■653 ▼aAlgebraic combinatorics
■653 ▼aAsymmetric simple exclusion process
■653 ▼aEhrhart theory
■653 ▼aMarkov chains
■653 ▼aPolyhedral geometry
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■690 ▼a0463
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357595▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
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