Mathematics – Probability
Scientific paper
2010-06-21
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This paper has been withdrawn by the authors. 5 pages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.
de Lima Bernardo N. B.
Sanchis Rémy
Silva Roger W. C.
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