Clustering in a continuum percolation model

J. Quintanilla; S. Torquato

doi:10.1017/S0001867800028019

Clustering in a continuum percolation model

J. Quintanilla, S. Torquato

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters of k balls (called k-mers) in the system, first rigorously derived by Penrose [15]. Our integral expressions are free of inherent redundancies, making them more tractable for numerical evaluation. We also derive and evaluate an integral expression for the average volume of k-mers.

Original language	English (US)
Pages (from-to)	327-336
Number of pages	10
Journal	Advances in Applied Probability
Volume	29
Issue number	2
DOIs	https://doi.org/10.1017/S0001867800028019
State	Published - Jun 1997

All Science Journal Classification (ASJC) codes

Statistics and Probability
Applied Mathematics

Keywords

Boolean model
Cluster properties

Access to Document

10.1017/S0001867800028019

Cite this

@article{ebe802aeff6345fa8695179229ccb312,

title = "Clustering in a continuum percolation model",

abstract = "We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters of k balls (called k-mers) in the system, first rigorously derived by Penrose [15]. Our integral expressions are free of inherent redundancies, making them more tractable for numerical evaluation. We also derive and evaluate an integral expression for the average volume of k-mers.",

keywords = "Boolean model, Cluster properties",

author = "J. Quintanilla and S. Torquato",

year = "1997",

month = jun,

doi = "10.1017/S0001867800028019",

language = "English (US)",

volume = "29",

pages = "327--336",

journal = "Advances in Applied Probability",

issn = "0001-8678",

publisher = "University of Sheffield",

number = "2",

}

TY - JOUR

T1 - Clustering in a continuum percolation model

AU - Quintanilla, J.

AU - Torquato, S.

PY - 1997/6

Y1 - 1997/6

N2 - We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters of k balls (called k-mers) in the system, first rigorously derived by Penrose [15]. Our integral expressions are free of inherent redundancies, making them more tractable for numerical evaluation. We also derive and evaluate an integral expression for the average volume of k-mers.

AB - We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters of k balls (called k-mers) in the system, first rigorously derived by Penrose [15]. Our integral expressions are free of inherent redundancies, making them more tractable for numerical evaluation. We also derive and evaluate an integral expression for the average volume of k-mers.

KW - Boolean model

KW - Cluster properties

UR - http://www.scopus.com/inward/record.url?scp=0012245601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012245601&partnerID=8YFLogxK

U2 - 10.1017/S0001867800028019

DO - 10.1017/S0001867800028019

M3 - Article

AN - SCOPUS:0012245601

SN - 0001-8678

VL - 29

SP - 327

EP - 336

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 2

ER -

Clustering in a continuum percolation model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this