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Multinomial Trees and Multinomial Percolation
Multinomial Trees and Multinomial Percolation
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103032
- ISBN
- 9798286442195
- DDC
- 510
- 저자명
- Tienni, Michele.
- 서명/저자
- Multinomial Trees and Multinomial Percolation
- 발행사항
- [Sl] : Yale University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 136 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Kenyon, Richard.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2025.
- 초록/해제
- 요약We study multinomial percolation, which is bond percolation on a family of graphs ("blow-up graphs") defined in terms of a fixed graph G. We compute connection thresholds in terms of distances on G. Moreover, if the percolation probability is inversely proportional to the blow-up multiplicity, there is a phase transition above which a giant component emerges. We show that many properties of the giant component can be computed using an analytic function with variables indexed by the vertices of G. Moreover, we find that the giant component gives rise to a natural field on G. As the blow-up multiplicity grows, we show that this field converges to a Gaussian field, and its covariance is given by the square of a massive Green's function on G.The main tool to prove the results above is the combinatorics of trees on blowup graphs ("multinomial trees"). To this end, the first half of this thesis is dedicated to the theory of multinomial trees. This includes two parts. Enumeration results show that the asymptotic growth of such trees are given by relative entropies of certain distributions on G. Analytic results show that the multivariate exponential generating function for rooted multinomial trees has analytic properties that can be formulated in terms of a massive Laplacian operator on G.
- 일반주제명
- Mathematics
- 일반주제명
- Statistical physics
- 일반주제명
- Applied mathematics
- 키워드
- Percolation
- 키워드
- Random graph
- 키워드
- Random walk
- 키워드
- Spanning tree
- 기타저자
- Yale University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■007cr#unu||||||||
■020 ▼a9798286442195
■035 ▼a(MiAaPQ)AAI31845964
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aTienni, Michele.
■24510▼aMultinomial Trees and Multinomial Percolation
■260 ▼a[Sl]▼bYale University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a136 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Kenyon, Richard.
■5021 ▼aThesis (Ph.D.)--Yale University, 2025.
■520 ▼aWe study multinomial percolation, which is bond percolation on a family of graphs ("blow-up graphs") defined in terms of a fixed graph G. We compute connection thresholds in terms of distances on G. Moreover, if the percolation probability is inversely proportional to the blow-up multiplicity, there is a phase transition above which a giant component emerges. We show that many properties of the giant component can be computed using an analytic function with variables indexed by the vertices of G. Moreover, we find that the giant component gives rise to a natural field on G. As the blow-up multiplicity grows, we show that this field converges to a Gaussian field, and its covariance is given by the square of a massive Green's function on G.The main tool to prove the results above is the combinatorics of trees on blowup graphs ("multinomial trees"). To this end, the first half of this thesis is dedicated to the theory of multinomial trees. This includes two parts. Enumeration results show that the asymptotic growth of such trees are given by relative entropies of certain distributions on G. Analytic results show that the multivariate exponential generating function for rooted multinomial trees has analytic properties that can be formulated in terms of a massive Laplacian operator on G.
■590 ▼aSchool code: 0265.
■650 4▼aMathematics
■650 4▼aStatistical physics
■650 4▼aApplied mathematics
■653 ▼aGenerating function
■653 ▼aLaplacian operator
■653 ▼aPercolation
■653 ▼aRandom graph
■653 ▼aRandom walk
■653 ▼aSpanning tree
■690 ▼a0405
■690 ▼a0217
■690 ▼a0364
■71020▼aYale University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356770▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
