%0 Journal Article
%T Monotonicity of Percolation Probability on $\Z^d$ with Long Range Connections
%A Bernardo N. B. de Lima
%A R¨Śmy Sanchis
%A Roger W. C. Silva
%J Mathematics
%D 2010
%I arXiv
%X Consider an independent site percolation model on $\Z^d,\ d\geq 2$, with parameter $p \in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to some coordinate axis. We show that the percolation probability is a non-decreasing function of $k$. We also generalize this result for models whose long range bonds have several lengths.
%U http://arxiv.org/abs/1006.4191v3