On Long Range Percolation with Heavy Tails

Details On Long Range Percolation with Heavy Tails On Long Range Percolation with Heavy Tails

2004-09-14

arxiv.org/abs/math/0409225v1

Mathematics

Probability

Scientific paper

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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