We study the Sine-Gordon model for $\beta^{2}< 4 \pi$ in infinite volume. We
give a variatonal characterization of it’s laplace transform, and deduce from
this large deviations. Along the way we obtain estimates which are strong
enough to obtain a proof of the Osterwalder-Schrader axioms including
exponential decay of correlations as a byproduct. Our method is based on the
Boue-Dupuis formula with an emphasis on the stochastic control structure of the
problem.
