The random connection model in high dimensions

Ronald Meester, Mathew D. Penrose and Anish Sarkar

Statistics & Probability Letters, 1997, vol. 35, issue 2, 145-153

Abstract: Consider a continuum percolation model in which each pair of points of a d-dimensional Poisson process of intensity [lambda] is connected with a probability which is a function g of the distance between them. We show that under a mild regularity condition on g, the critical value of [lambda], above which an infinite cluster exists a.s., is asymptotic to ([integral operator]Rd g(x)dx)-1 as d --> [infinity].

Keywords: Continuum; percolation; Critical; value; High; dimensions (search for similar items in EconPapers)
Date: 1997
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