Christian Maes, Frank Redig, Senya Shlosman,, Annelies Van Moffaert
Percolation, Path Large Deviations and Weak Gibbsianity
(293K, Postscript)

ABSTRACT.  We present a unified approach to establishing the Gibbsian character of a
wide class of non-Gibbsian states, arising in the Renormalisation Group
theory. Within the realm of the Pirogov-Sinai theory for lattice spin
systems, we prove that RG transformations applied to low temperature 
phases give rise to weakly Gibbsian measures. In other words, we show that
the Griffiths-Pearce-Israel scenario of RG pathologies is carried by
atypical configurations. The renormalized measures are described by an
effective Gibbsian interaction, with relative energies well-defined on a
full measure set of configurations. In this way we complete the first part
of the Dobrushin Restoration Program: to give a Gibbsian description to 
non-Gibbsian states. A disagreement percolation estimate is used in the 
proof to bound the decay of quenched correlations through which the
interaction potential is constructed. The percolation is controlled via a
novel type of pathwise large deviation theory.