Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses

Research output: Contribution to journalArticle

Abstract

We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,... K} and prove both that percolation occurs and that the infinite component is unique for V=ℤ2×{0,1} or larger.

Original languageEnglish (US)
Pages (from-to)511-527
Number of pages17
JournalProbability Theory and Related Fields
Volume92
Issue number4
DOIs
StatePublished - Dec 1992

Fingerprint

Spin Glass
Random Graphs
Uniqueness
Range of data
Nearest Neighbor
Cover
Dependent
Theorem
Model

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

@article{d3f5f2b7ba8e4bd7b84e41a135f1633d,
title = "Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses",
abstract = "We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,... K} and prove both that percolation occurs and that the infinite component is unique for V=ℤ2×{0,1} or larger.",
author = "Alberto Gandolfi and Keane, {M. S.} and Charles Newman",
year = "1992",
month = "12",
doi = "10.1007/BF01274266",
language = "English (US)",
volume = "92",
pages = "511--527",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses

AU - Gandolfi, Alberto

AU - Keane, M. S.

AU - Newman, Charles

PY - 1992/12

Y1 - 1992/12

N2 - We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,... K} and prove both that percolation occurs and that the infinite component is unique for V=ℤ2×{0,1} or larger.

AB - We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on ℤd or ℤd × ℕ with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on ℤd or on a slab ℤd × {0,... K} and prove both that percolation occurs and that the infinite component is unique for V=ℤ2×{0,1} or larger.

UR - http://www.scopus.com/inward/record.url?scp=0001295837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001295837&partnerID=8YFLogxK

U2 - 10.1007/BF01274266

DO - 10.1007/BF01274266

M3 - Article

VL - 92

SP - 511

EP - 527

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 4

ER -