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arXiv · 1805.10814

A variational method for $\Phi^4_3$

N. Barashkov·M. Gubinelli
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Abstract

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.

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N. Barashkov, M. Gubinelli. 2018-05-28. A variational method for $\Phi^4_3$. https://doi.org/10.1215/00127094-2020-0029

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