 9416 Marchetti D.H.U.
 UPPER BOUND ON THE TRUNCATED CONNECTIVITY
IN ONEDIMENIONAL BETA /xy^2 PERCOLATION MODELS
AT BETA LARGER THAN 1
(59K, LaTeX)
Jan 21, 94

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Abstract. We consider onedimensional FortuinKasteleyn percolation models generated
by the bond occupation probabilities
$$
p_{(xy)}={\cases{p & if $xy=1$ \cr
1e^{\beta / xy^2} & otherwise \cr}}
$$
and a real parameter $\kappa $. We prove that for any $\beta >1$ and $\kappa
\geq 1$ the percolation density $M$ is strictly positive provided $p$ is
sufficiently close to 1. We also prove, under the same assumptions, that the
following upper bound for the truncated connectivity
$$
\tau ^{\prime }(x,y)\leq Cxy^{\overline{\theta }}
$$
holds with $\overline{\theta }=\min (2(\beta \eta 1),2)$ where $\eta
=\eta (p)\nearrow 1$ as $p\nearrow 1$.
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