Open Access
May 2015 Introduction to regularity structures
Martin Hairer
Braz. J. Probab. Stat. 29(2): 175-210 (May 2015). DOI: 10.1214/14-BJPS241


These are short notes from a series of lectures given at the University of Rennes in June 2013, at the University of Bonn in July 2013, at the XVIIth Brazilian School of Probability in Mambucaba in August 2013, and at ETH Zurich in September 2013. They give a concise overview of the theory of regularity structures as exposed in the article [Invent. Math. DOI: 10.1007/s00222-014-0505-4]. In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified. We focus on applying the theory to the problem of giving a solution theory to the stochastic quantisation equations for the Euclidean $\Phi^{4}_{3}$ quantum field theory.


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Martin Hairer. "Introduction to regularity structures." Braz. J. Probab. Stat. 29 (2) 175 - 210, May 2015.


Published: May 2015
First available in Project Euclid: 15 April 2015

zbMATH: 1316.81061
MathSciNet: MR3336866
Digital Object Identifier: 10.1214/14-BJPS241

Keywords: Regularity structures , renormalisation , stochastic PDEs

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 2 • May 2015
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