N. Barashkov and M. Gubinelli
We introduce an explicit description of the $\Phi^4_3$ 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, $\Gamma$-convergence allows to extend the variational characterization to the unregularized model.
N. Barashkov and M. Gubinelli. A variational method for $\Phi^4_3$. Papers of Massimiliano Gubinelli, 2018, version 2. https://mgubi.org/papers/paper/phi43-variational/
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