Stochastic analysis: around the KPZ universality class. Abstracts from the workshop held June 1--7, 2014.
type: Item
instance of: scholarly article
title: Stochastic analysis: around the KPZ universality class. Abstracts from the workshop held June 1--7, 2014.
zbMATH Open document ID: 1349.00176
DOI: 10.4171/OWR/2014/28
published in: Oberwolfach Reports
publication date: 2016-11-30T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 60-06
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35-06
Mathematics Subject Classification ID: 60B20
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B23
zbMATH DE Number: 6658010
MaRDI profile type: Publication
cites work: Shape fluctuations and random matrices
cites work: A Fredholm determinant representation in ASEP
cites work: Asymptotics in ASEP with step initial condition
cites work: On ASEP with step Bernoulli initial condition
full work available at URL: https://doi.org/10.4171/owr/2014/28
OpenAlex ID: W2041501288
description: scientific article; zbMATH DE number 6658010