English

Renormalization Group and Stochastic PDE's

Probability 2015-02-20 v2 Mathematical Physics math.MP

Abstract

We develop a Renormalization Group (RG) approach to the study of existence and uniqueness of solutions to stochastic partial differential equations driven by space-time white noise. As an example we prove well-posedness and independence of regularization for the ϕ4\phi^4 model in three dimensions recently studied by Hairer. Our method is "Wilsonian": the RG allows to construct effective equations on successive space time scales. Renormalization is needed to control the parameters in these equations. In particular no theory of multiplication of distributions enters our approach.

Keywords

Cite

@article{arxiv.1410.3094,
  title  = {Renormalization Group and Stochastic PDE's},
  author = {Antti Kupiainen},
  journal= {arXiv preprint arXiv:1410.3094},
  year   = {2015}
}

Comments

31 pages. Revised version with comments and references added and Lemma 10 corrected and absorbed to Proposition 11

R2 v1 2026-06-22T06:20:46.213Z