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Hierarchical Discrete Gaussian Model
Hierarchical Discrete Gaussian Model
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103632
- ISBN
- 9798315791195
- DDC
- 510
- 저자명
- Huang, Haiyu.
- 서명/저자
- Hierarchical Discrete Gaussian Model
- 발행사항
- [Sl] : University of California, Los Angeles, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 230 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Biskup, Marek.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Los Angeles, 2025.
- 초록/해제
- 요약Given a square box Λn ⊆ Z2 of side-length Ln with L, n 1, we study hierarchical random fields {ϕx : x ∈ Λn} with law proportional to e1/2 β(φ,∆nϕ) ∏x∈Λn ν(dϕx), where β 0 is the inverse temperature, ∆n is a hierarchical Laplacian on Λn, and ν is a non-degenerate 1-periodic measure on R. Our primary object of interest is the Discrete Gaussian (DG) model(also known as integer-valued Gaussian Free Field), where ν is the counting measure on Z.Relying on renormalization group (RG) analysis, we derive sharp asymptotic formulas, in the limit as n → ∞, for the covariance ⟨ϕxϕy⟩ and the fractional charge correlation ⟨e2πiα(ϕx −ϕy)⟩ in the subcritical β βc regimes. The field exhibits logarithmic correlations throughout, albeit with a distinct β-dependence of the variance and fractional-charge exponents in the subcritical and supercritical regimes. Explicit logarithmic corrections appear at the critical point.We also study the extremal properties of the hierarchical DG model throughout the subcritical regime. For β ∈ (0, βc) denoting mn := β−1/2[(4 log L)1/2n − 3/2 (4 log L)−1/2 log n], we prove that, along increasing sequences of n such that the fractional part of mn converges to s ∈ [0, 1), the centered maximum maxx∈Λn ϕx − ⌊mn⌋ converges in law to a discrete variant of a randomly shifted Gumbel law with the shift depending non-trivially on s. The convergence extends to the extremal process whose law tends to a decorated Poisson point process with a random intensity measure.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Physics
- 키워드
- Probability
- 기타저자
- University of California, Los Angeles Mathematics 0540
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103632
■006m o d
■007cr#unu||||||||
■020 ▼a9798315791195
■035 ▼a(MiAaPQ)AAI32046996
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aHuang, Haiyu.
■24510▼aHierarchical Discrete Gaussian Model
■260 ▼a[Sl]▼bUniversity of California, Los Angeles▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a230 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Biskup, Marek.
■5021 ▼aThesis (Ph.D.)--University of California, Los Angeles, 2025.
■520 ▼aGiven a square box Λn ⊆ Z2 of side-length Ln with L, n 1, we study hierarchical random fields {ϕx : x ∈ Λn} with law proportional to e1/2 β(φ,∆nϕ) ∏x∈Λn ν(dϕx), where β 0 is the inverse temperature, ∆n is a hierarchical Laplacian on Λn, and ν is a non-degenerate 1-periodic measure on R. Our primary object of interest is the Discrete Gaussian (DG) model(also known as integer-valued Gaussian Free Field), where ν is the counting measure on Z.Relying on renormalization group (RG) analysis, we derive sharp asymptotic formulas, in the limit as n → ∞, for the covariance ⟨ϕxϕy⟩ and the fractional charge correlation ⟨e2πiα(ϕx −ϕy)⟩ in the subcritical β βc regimes. The field exhibits logarithmic correlations throughout, albeit with a distinct β-dependence of the variance and fractional-charge exponents in the subcritical and supercritical regimes. Explicit logarithmic corrections appear at the critical point.We also study the extremal properties of the hierarchical DG model throughout the subcritical regime. For β ∈ (0, βc) denoting mn := β−1/2[(4 log L)1/2n − 3/2 (4 log L)−1/2 log n], we prove that, along increasing sequences of n such that the fractional part of mn converges to s ∈ [0, 1), the centered maximum maxx∈Λn ϕx − ⌊mn⌋ converges in law to a discrete variant of a randomly shifted Gumbel law with the shift depending non-trivially on s. The convergence extends to the extremal process whose law tends to a decorated Poisson point process with a random intensity measure.
■590 ▼aSchool code: 0031.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aPhysics
■653 ▼aMathematical physics
■653 ▼aProbability
■653 ▼aStatistical mechanics
■653 ▼aDiscrete Gaussian
■653 ▼aRenormalization group
■690 ▼a0405
■690 ▼a0642
■690 ▼a0605
■71020▼aUniversity of California, Los Angeles▼bMathematics 0540.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0031
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358019▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
