Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$

Details Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$ Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$

2006-05-15

arxiv.org/abs/math-ph/0605047v2

Physics

Mathematical Physics

6 pages

Scientific paper

10.1007/s10955-007-9347-4

In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $\tau_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.

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