JournalsowrVol. 11, No. 2pp. 1515–1568

Stochastic Analysis: Around the KPZ Universality Class

  • Alice Guionnet

    Massachusetts Institute of Technology, Cambridge, USA
  • Martin Hairer

    University of Warwick, Coventry, UK
  • Wendelin Werner

    ETH Zürich, Switzerland
Stochastic Analysis: Around the KPZ Universality Class cover

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Abstract

The Gaussian distribution is the “universal” distribution arising in a huge variety of contexts that describes the compound effect of the random fluctuations of many independent (or weakly dependent) sources of randomness that are combined in a (close to) additive way. While this has been very well understood for a long time, the last few years have seen an explosion of results around the “KPZ universality class”, which contains many systems where strongly interacting individual components are combined in a highly non-linear way. In this class, which is still rather poorly understood from a mathematical perspective, fluctuations typically exhibit scaling exponent 1/3 instead of the exponent 1/2 familiar from the central limit theorem and limiting distributions are of Tracy-Widom type rather than Gaussian.

This workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to the understanding of the KPZ equation and universality class. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to renormalisation theory, stochastic analysis, random matrix theory, classical probability theory, orthogonal polynomials, the theory of rough paths, etc.

Cite this article

Alice Guionnet, Martin Hairer, Wendelin Werner, Stochastic Analysis: Around the KPZ Universality Class. Oberwolfach Rep. 11 (2015), no. 2, pp. 1515–1568

DOI 10.4171/OWR/2014/28