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

Gastao A. Braga·Leandro M. Cioletti·Remy Sanchis
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Abstract

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 $τ_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.

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Gastao A. Braga, Leandro M. Cioletti, Remy Sanchis. 2007-09-10. Decay Properties of the Connectivity for Mixed Long Range Percolation Models on $\Z^d$. https://doi.org/10.1007/s10955-007-9347-4

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