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 \({\phi^4}\) model in three dimensions recently studied by Hairer and Catellier and Chouk. 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.
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Communicated by Abdelmalek Abdesselam.
Supported by Academy of Finland.
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Kupiainen, A. Renormalization Group and Stochastic PDEs. Ann. Henri Poincaré 17, 497–535 (2016). https://doi.org/10.1007/s00023-015-0408-y
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DOI: https://doi.org/10.1007/s00023-015-0408-y