The $\Phi^4_3$ measure via Girsanov's theorem

Nikolay Barashkov and Massimiliano Gubinelli

First issued 3 April 2020 · PDF · HTML

Abstract

We construct the $\Phi^4_3$ measure on a periodic three dimensional box as an absolutely continuous perturbation of a random shift of the Gaussian free field. The shifted measure is constructed via Girsanov's theorem and the relevant filtration is the one generated by a scale parameter. As a byproduct we give a self-contained proof that the $\Phi^4_3$ measure is singular wrt. the Gaussian free field.

Versions

1. Version 2 (arXiv v2) current
   20 May 2020
   arXiv comments: 28 pages, no figures, some typos corrected
   PDF · TeXmacs source · files and digests · arXiv:2004.01513
2. Version 1 (arXiv v1)
   3 April 2020
   arXiv comments: 27 pages, no figures
   PDF · TeXmacs source · files and digests · arXiv:2004.01513

Cite

Nikolay Barashkov and Massimiliano Gubinelli. The $\Phi^4_3$ measure via Girsanov's theorem. Papers of Massimiliano Gubinelli, 2020, version 2. https://mgubi.org/papers/paper/phi43-girsanov/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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