Monotonicity of Percolation Probability on $\Z^d$ with Long Range Connections

Details Monotonicity of Percolation Probability on $\Z^d$ with Long Range Connections Monotonicity of Percolation Probability on $\Z^d$ with Long Range Connections

2010-06-21

arxiv.org/abs/1006.4191v3

Mathematics

Probability

This paper has been withdrawn by the authors. 5 pages

Scientific paper

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.

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