On Long Range Percolation with Heavy Tails
Benoîte Borge de Lima (UFMG, Belo Horizonte)
Vladas Sidoravicius (IMPA, Rio de Janeiro)
Abstract
Consider independent long range percolation on $\mathbf{Z}^d$, $d\geq 2$, where edges of length $n$ are open with probability $p_n$. We show that if $\limsup_{n\to\infty}p_n > 0,$ then there exists an integer $N$ such that $P_N(0\leftrightarrow \infty) > 0$, where $P_N$ is the truncated measure obtained by taking $p_{N,n}=p_n$ for $n \leq N$ and $p_{N,n}=0$ for all $n > N$.
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Pages: 175-177
Publication Date: December 30, 2004
DOI: 10.1214/ECP.v9-1122
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