Existence of phase transition for heavy-tailed continuum percolation

A. Sapozhnikov

Existence of phase transition for heavy-tailed continuum percolation

A. Sapozhnikov

Eurandom

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Abstract

We consider a continuum percolation model in Rd, where d= 2. It is given by a homogeneous Poisson process of intensity ¿ and independent radii random variables of common distribution of a positive random variable r. Let ¿c be the critical intensity for the existence of infinite cluster. We provide conditions for positivety of ¿c. In case Er2d-1 = 8 our result is new.

Original language	English
Pages (from-to)	575-586
Journal	Markov Processes and Related Fields
Volume	13
Issue number	3
Publication status	Published - 2007

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title = "Existence of phase transition for heavy-tailed continuum percolation",

abstract = "We consider a continuum percolation model in Rd, where d= 2. It is given by a homogeneous Poisson process of intensity ¿ and independent radii random variables of common distribution of a positive random variable r. Let ¿c be the critical intensity for the existence of infinite cluster. We provide conditions for positivety of ¿c. In case Er2d-1 = 8 our result is new.",

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year = "2007",

language = "English",

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T1 - Existence of phase transition for heavy-tailed continuum percolation

AU - Sapozhnikov, A.

PY - 2007

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N2 - We consider a continuum percolation model in Rd, where d= 2. It is given by a homogeneous Poisson process of intensity ¿ and independent radii random variables of common distribution of a positive random variable r. Let ¿c be the critical intensity for the existence of infinite cluster. We provide conditions for positivety of ¿c. In case Er2d-1 = 8 our result is new.

AB - We consider a continuum percolation model in Rd, where d= 2. It is given by a homogeneous Poisson process of intensity ¿ and independent radii random variables of common distribution of a positive random variable r. Let ¿c be the critical intensity for the existence of infinite cluster. We provide conditions for positivety of ¿c. In case Er2d-1 = 8 our result is new.

M3 - Article

SN - 1024-2953

VL - 13

SP - 575

EP - 586

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

IS - 3

ER -

Existence of phase transition for heavy-tailed continuum percolation

Abstract

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