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Renormalisation of parabolic stochastic PDEs

  • Special Feature: The Takagi Lectures
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Japanese Journal of Mathematics Aims and scope

Abstract

We give a survey of recent result regarding scaling limits of systems from statistical mechanics, as well as the universality of the behaviour of such systems in so-called cross-over regimes. It transpires that some of these universal objects are described by singular stochastic PDEs. We then give a survey of the recently developed theory of regularity structures which allows to build these objects and to describe some of their properties. We place particular emphasis on the renormalisation procedure required to give meaning to these equations.

These are expanded notes of the 20th Takagi Lectures held at The University of Tokyo on November 4, 2017.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK

    Martin Hairer

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  1. Martin Hairer
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Correspondence to Martin Hairer.

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Communicated by: Takashi Kumagai

This article is based on the 20th Takagi Lectures that the author delivered at the University of Tokyo on November 4, 2017.

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Hairer, M. Renormalisation of parabolic stochastic PDEs. Jpn. J. Math. 13, 187–233 (2018). https://doi.org/10.1007/s11537-018-1742-x

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  • DOI: https://doi.org/10.1007/s11537-018-1742-x

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