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Introduction to Regularity Structures
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abstract
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. We give a concise overview of the theory of regularity structures as exposed in Hairer (2014). 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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Cited by 1 Pith paper
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Lecture notes on the flow equation approach to singular stochastic PDEs
A scale-by-scale flow equation with suitably chosen counterterms constructs renormalized solutions of fractional elliptic Phi^4 SPDEs throughout the subcritical regime.
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