A variational method for Φ 3 4

Abstract

We introduce an explicit description of the Φ 3 4 measure on a bounded domain. Our starting point is the interpretation of its Laplace transform as the value function of a stochastic optimal control problem along the flow of a scale regularization parameter. Once small scale singularities have been renormalized by the standard counterterms, Γ -convergence allows us to extend the variational characterization to the unregularized model.