Pfister C.-E., Vande Velde K.
Almost sure quasilocality in the random cluster model
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ABSTRACT.  We investigate the Gibbsian nature of the random cluster measures
$\mu ^{q,p}$ and $\tilde{\mu ^{q,p}}$, obtained as infinite-volume limit
of finite volume measures with free and wired boundary conditions.
For $q>1$,
the measures are not  Gibbs measures, but
it turns out that the conditional distribution on one edge, given the
configuration outside that edge is almost surely quasilocal.