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Exponential Last Passage Percolation in the Upper Large Deviation Regime and Multi-Point Distributions for Other LPP Models
Exponential Last Passage Percolation in the Upper Large Deviation Regime and Multi-Point Distributions for Other LPP Models
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105240
- ISBN
- 9798291569252
- DDC
- 510
- 서명/저자
- Exponential Last Passage Percolation in the Upper Large Deviation Regime and Multi-Point Distributions for Other LPP Models
- 발행사항
- [Sl] : University of Michigan, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 217 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: Baik, Jinho.
- 학위논문주기
- Thesis (Ph.D.)--University of Michigan, 2025.
- 초록/해제
- 요약This thesis focuses on the study of directed last passage percolation (LPP) models in random media, which are two-dimensional stochastic growth models. These models have numerous applications and exhibit deep connections with random matrix theory and integrable probability. A key quantity in these models is the last passage time, which represents the maximum total weight collected along an up-right path between two points. After appropriate scaling, it has been shown that the last passage time field converges to a universal limit, known as the KPZ fixed point. The thesis is divided into two parts.The first part of this thesis studies exponential LPP under the condition that the last passage time at one point is unusually large. We then analyz effect of this conditioning on the last passage time at other points. We find that this conditioning influences the last passage times in certain regions. After applying a suitable scaling, which differs from the 1:2:3 KPZ scaling, we also derive results for the conditional fluctuations.The second part of the thesis is devoted to computing the multi-point distributions for Poissonian and Brownian LPP with step initial condition. Using these explicit formulas, we provide an alternative proof that the multi-point distributions of Poissonian and Brownian LPP converge to those of the KPZ fixed point under the 1:2:3 scaling.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Conditional law
- 기타저자
- University of Michigan Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798291569252
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■035 ▼a(MiAaPQ)umichrackham006496
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aTripathi, Tejaswi.
■24510▼aExponential Last Passage Percolation in the Upper Large Deviation Regime and Multi-Point Distributions for Other LPP Models
■260 ▼a[Sl]▼bUniversity of Michigan▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a217 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: Baik, Jinho.
■5021 ▼aThesis (Ph.D.)--University of Michigan, 2025.
■520 ▼aThis thesis focuses on the study of directed last passage percolation (LPP) models in random media, which are two-dimensional stochastic growth models. These models have numerous applications and exhibit deep connections with random matrix theory and integrable probability. A key quantity in these models is the last passage time, which represents the maximum total weight collected along an up-right path between two points. After appropriate scaling, it has been shown that the last passage time field converges to a universal limit, known as the KPZ fixed point. The thesis is divided into two parts.The first part of this thesis studies exponential LPP under the condition that the last passage time at one point is unusually large. We then analyz effect of this conditioning on the last passage time at other points. We find that this conditioning influences the last passage times in certain regions. After applying a suitable scaling, which differs from the 1:2:3 KPZ scaling, we also derive results for the conditional fluctuations.The second part of the thesis is devoted to computing the multi-point distributions for Poissonian and Brownian LPP with step initial condition. Using these explicit formulas, we provide an alternative proof that the multi-point distributions of Poissonian and Brownian LPP converge to those of the KPZ fixed point under the 1:2:3 scaling.
■590 ▼aSchool code: 0127.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aApplied mathematics
■653 ▼aDirected last passage percolation
■653 ▼aConditional law
■653 ▼aConditional fluctuations
■653 ▼aMulti-point distribution
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aUniversity of Michigan▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0127
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359954▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
