 04285 Friedli S., de Lima B.N.B, Sidoravicius V.
 On Long Range Percolation with Heavy Tails
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Sep 14, 04

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Abstract. Consider independent long range percolation on $\mathbf{Z}^2$,
where horizontal and vertical 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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