Existence of Phase Transition for Heavy-Tailed Continuum Percolation
A. Sapozhnikov
2007, v.13, Issue 3, 575-586
ABSTRACT
We consider a continuum percolation model in $\r^d$, where $d\geq 2$. It is given by a homogeneous Poisson process of intensity $\lambda$ and independent radii random variables of common distribution of a positive random variable $r$. Let $\lambda_c$ be the critical intensity for the existence of infinite cluster. We provide conditions for positivity of $\lambda_c$. In case ${\math E}r^{2d-1} = \infty$ our result is new.
Keywords: continuum percolation,percolation,long-range percolation,connectivity,critical density,moments
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