Existence of phase transition for heavy-tailed continuum percolation

A. Sapozhnikov

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)575-586
JournalMarkov Processes and Related Fields
Volume13
Issue number3
Publication statusPublished - 2007

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