Infinite clusters in percolation models

C. M. Newman; L. S. Schulman

doi:10.1007/BF01011437

Infinite clusters in percolation models

C. M. Newman, L. S. Schulman

Mathematics

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Abstract

The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown that N₀, the number of distinct infinite clusters, is either 0, 1, or ∞ and the case N₀=∞ (which might occur in sufficiently high dimension) is analyzed.

Original language	English (US)
Pages (from-to)	613-628
Number of pages	16
Journal	Journal of Statistical Physics
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/BF01011437
State	Published - Nov 1981

Keywords

Percolation
cluster density
infinite clusters
surface-to-volume ratio

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01011437

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abstract = "The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown that N0, the number of distinct infinite clusters, is either 0, 1, or ∞ and the case N0=∞ (which might occur in sufficiently high dimension) is analyzed.",

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author = "Newman, {C. M.} and Schulman, {L. S.}",

year = "1981",

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AU - Newman, C. M.

AU - Schulman, L. S.

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N2 - The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown that N0, the number of distinct infinite clusters, is either 0, 1, or ∞ and the case N0=∞ (which might occur in sufficiently high dimension) is analyzed.

AB - The qualitative nature of infinite clusters in percolation models is investigated. The results, which apply to both independent and correlated percolation in any dimension, concern the number and density of infinite clusters, the size of their external surface, the value of their (total) surface-to-volume ratio, and the fluctuations in their density. In particular it is shown that N0, the number of distinct infinite clusters, is either 0, 1, or ∞ and the case N0=∞ (which might occur in sufficiently high dimension) is analyzed.

KW - Percolation

KW - cluster density

KW - infinite clusters

KW - surface-to-volume ratio

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ER -

Infinite clusters in percolation models

Abstract

Keywords

ASJC Scopus subject areas

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