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

Braga, Gastao A.; Cioletti, Leandro M.; Sanchis, Remy

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

Authors

Braga, Gastao A.

Cioletti, Leandro M.

Sanchis, Remy

Description

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.
6 pages