On Long Range Percolation with Heavy Tails
Sacha Friedli, IMPA, Rio de Janeiro
Bernardo Nunes Borge de Lima, UFMG, Belo Horizonte
Vladas Sidoravicius, IMPA, Rio de Janeiro
Abstract
Consider independent long range percolation on $mathbf{Z}^d$, $dgeq
2$,
where edges of length $n$ are open with
probability $p_n$. We show that if
$limsup_{ntoinfty}p_n>0,$ then there
exists an integer $N$ such that $P_N(0leftrightarrow infty)>0$,
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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