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arXiv:1805.10814math.PR

A variational method for $Φ^4_3$

N. Barashkov, M. Gubinelli

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Abstract

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.

arXiv comments
47 pages, added proof of Gamma-convergence, title changed
Journal reference
Duke Math. J. 169, no. 17 (2020), 3339-3415
DOI
doi:10.1215/00127094-2020-0029
Subjects
math.PRProbability math-phMathematical Physics

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    • I generally use TeXmacs for notes, derivations, lectures, articles, all, of course. Most of my papers in the last 7 years, around 15 and all my lectures in the same period, circa 2 courses a year. More in detail, all these papers are been written completely in TeXmacs and then…

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