A variational method for $Φ^4_3$
We introduce an explicit description of the $Φ^4_3$ 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 to extend the variational characterization to the unregularized model.
math.PR↗