  We present a new approach to study measures on ensembles of contours,
polymers or other objects interacting by some sort of exclusion condition. For
concreteness we develop it here for the case of Peierls contours. Unlike
existing methods, which are based on cluster-expansion formalisms and/or
complex analysis, our method is strictly probabilistic and hence can be applied
even in the absence of analyticity properties. It involves a Harris graphical
construction of a loss network for which the measure of interest is invariant.
The existence of the process and its mixing properties depend on the absence of
infinite clusters for a dual (backwards) oriented percolation process which we
dominate by a multitype branching process. Within the region of subcriticality
of this branching process the approach yields: (i) exponential convergence to
the equilibrium (=contour) measures, (ii) standard clustering and finite-effect
properties of the contour measure, (iii) a particularly strong form of the
central limit theorem, and (iv) a Poisson approximation for the distribution of
contours at low temperature.
