### Abstract

Properties of infinite clusters in general percolation models are investigated. The number of infinite clusters is either zero, one or infinity. Results are found on the density of the various kinds of infinite clusters. In particular, 'filamentary' and 'rough' clusters, which individually do not have non-zero density, are studied with an eye toward ascertaining whether these exist in some models, and hence whether an infinity of infinite clusters is possible. Conjectures are presented on the behaviour of systems with an infinity of infinite clusters under scale transformations, and also on the way in which the presence of such clusters influences the prevalence of large finite clusters.

Original language | English (US) |
---|---|

Article number | 028 |

Pages (from-to) | 1735-1743 |

Number of pages | 9 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 14 |

Issue number | 7 |

DOIs | |

State | Published - 1981 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*14*(7), 1735-1743. [028]. https://doi.org/10.1088/0305-4470/14/7/028

**Number and density of percolating clusters.** / Newman, Charles; Schulman, L. S.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 14, no. 7, 028, pp. 1735-1743. https://doi.org/10.1088/0305-4470/14/7/028

}

TY - JOUR

T1 - Number and density of percolating clusters

AU - Newman, Charles

AU - Schulman, L. S.

PY - 1981

Y1 - 1981

N2 - Properties of infinite clusters in general percolation models are investigated. The number of infinite clusters is either zero, one or infinity. Results are found on the density of the various kinds of infinite clusters. In particular, 'filamentary' and 'rough' clusters, which individually do not have non-zero density, are studied with an eye toward ascertaining whether these exist in some models, and hence whether an infinity of infinite clusters is possible. Conjectures are presented on the behaviour of systems with an infinity of infinite clusters under scale transformations, and also on the way in which the presence of such clusters influences the prevalence of large finite clusters.

AB - Properties of infinite clusters in general percolation models are investigated. The number of infinite clusters is either zero, one or infinity. Results are found on the density of the various kinds of infinite clusters. In particular, 'filamentary' and 'rough' clusters, which individually do not have non-zero density, are studied with an eye toward ascertaining whether these exist in some models, and hence whether an infinity of infinite clusters is possible. Conjectures are presented on the behaviour of systems with an infinity of infinite clusters under scale transformations, and also on the way in which the presence of such clusters influences the prevalence of large finite clusters.

UR - http://www.scopus.com/inward/record.url?scp=27644599414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644599414&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/14/7/028

DO - 10.1088/0305-4470/14/7/028

M3 - Article

VL - 14

SP - 1735

EP - 1743

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

M1 - 028

ER -