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Dynamical and Static Aspects of Interacting Particle Systems
Dynamical and Static Aspects of Interacting Particle Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103052
- ISBN
- 9798286427406
- DDC
- 510
- 서명/저자
- Dynamical and Static Aspects of Interacting Particle Systems
- 발행사항
- [Sl] : New York University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 213 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Lubetzky, Eyal.
- 학위논문주기
- Thesis (Ph.D.)--New York University, 2025.
- 초록/해제
- 요약In this dissertation, we study two models of interacting particle systems: one from a dynamical perspective, where the system evolves under a specified law and we are concerned with the evolution of the system over time; the other from a static perspective, where we answer questions regarding the typical states of the system.The first is the Noisy Voter model, a dynamical system widely studied in natural and social sciences which bears connections with the stochastic Ising and Potts models. Using duality with a system of coalescing random walks, regularity of the auto-correlation and conductance bounds, we find precise asymptotics for the mixing time of the system and its exact relation to the starting state, on any graph with sub-exponential growth rate of balls.The second model that we consider is the (2+1)D Solid-On-Solid model. The low-temperature SOS model on a box of side L with 0 boundary conditions and a floor at height 0 typically admits ≍ log L nested macroscopic level line loops. The vertical displacement ρ of the top level line L0 from the bottom side of the box is expected to behave like a variant of a Ferrari-Spohn diffusion on an interval I0 of size L2/3 at the center of the side, after rescaling I0 by L2/3 and ρ by L1/3. Using the Ornstein-Zernike machinery and a known result ruling out pinning of Ising polymers with modified interactions along the boundary, we show that the above rescaling of ρ essentially dominates a Ferrari-Spohn diffusion, and prove a lower bound of the predicted order L1/3.
- 일반주제명
- Mathematics
- 일반주제명
- Statistical physics
- 일반주제명
- High temperature physics
- 키워드
- Graph theory
- 키워드
- Ising model
- 키워드
- Random walks
- 키워드
- Voter model
- 기타저자
- New York University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103052
■006m o d
■007cr#unu||||||||
■020 ▼a9798286427406
■035 ▼a(MiAaPQ)AAI31931935
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aCaddeo, Patrizio.
■24510▼aDynamical and Static Aspects of Interacting Particle Systems
■260 ▼a[Sl]▼bNew York University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a213 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Lubetzky, Eyal.
■5021 ▼aThesis (Ph.D.)--New York University, 2025.
■520 ▼aIn this dissertation, we study two models of interacting particle systems: one from a dynamical perspective, where the system evolves under a specified law and we are concerned with the evolution of the system over time; the other from a static perspective, where we answer questions regarding the typical states of the system.The first is the Noisy Voter model, a dynamical system widely studied in natural and social sciences which bears connections with the stochastic Ising and Potts models. Using duality with a system of coalescing random walks, regularity of the auto-correlation and conductance bounds, we find precise asymptotics for the mixing time of the system and its exact relation to the starting state, on any graph with sub-exponential growth rate of balls.The second model that we consider is the (2+1)D Solid-On-Solid model. The low-temperature SOS model on a box of side L with 0 boundary conditions and a floor at height 0 typically admits ≍ log L nested macroscopic level line loops. The vertical displacement ρ of the top level line L0 from the bottom side of the box is expected to behave like a variant of a Ferrari-Spohn diffusion on an interval I0 of size L2/3 at the center of the side, after rescaling I0 by L2/3 and ρ by L1/3. Using the Ornstein-Zernike machinery and a known result ruling out pinning of Ising polymers with modified interactions along the boundary, we show that the above rescaling of ρ essentially dominates a Ferrari-Spohn diffusion, and prove a lower bound of the predicted order L1/3.
■590 ▼aSchool code: 0146.
■650 4▼aMathematics
■650 4▼aStatistical physics
■650 4▼aHigh temperature physics
■653 ▼aGraph theory
■653 ▼aInteracting particle systems
■653 ▼aIsing model
■653 ▼aRandom walks
■653 ▼aVoter model
■690 ▼a0405
■690 ▼a0217
■690 ▼a0597
■71020▼aNew York University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0146
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356867▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
