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Renormalisation of parabolic stochastic PDEs

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Title: Renormalisation of parabolic stochastic PDEs
Authors: Hairer, M
Item Type: Journal Article
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.
Issue Date: 1-Sep-2018
Date of Acceptance: 19-Jun-2018
URI: http://hdl.handle.net/10044/1/64263
DOI: https://dx.doi.org/10.1007/s11537-018-1742-x
ISSN: 0289-2316
Publisher: Springer Verlag
Start Page: 187
End Page: 233
Journal / Book Title: Japanese Journal of Mathematics
Volume: 13
Issue: 2
Copyright Statement: © The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature. The final publication is available at Springer via https://dx.doi.org/10.1007/s11537-018-1742-x
Keywords: Science & Technology
Physical Sciences
Mathematics
stochastic PDEs
renormalisation
regularity structures
UNIVERSALITY CLASS
INVARIANT-MEASURES
PARTICLE-SYSTEMS
EQUATIONS DRIVEN
SIMPLE EXCLUSION
SCALING LIMITS
KPZ EQUATION
FLUCTUATIONS
PERCOLATION
BEHAVIOR
math.PR
math-ph
math.AP
math.MP
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2018-08-02
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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