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On Long Range Percolation with Heavy Tails
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Sacha Friedli, IMPA, Rio de Janeiro
Bernardo Nunes Borge de Lima, UFMG, Belo Horizonte
Vladas Sidoravicius, IMPA, Rio de Janeiro
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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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Full text: PDF
Pages: 175-177
Published on: December 30, 2004
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Electronic Communications in Probability. ISSN: 1083-589X |
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