Fluctuation exponent of the KPZ/stochastic Burgers equation

Marton Balazs, Jeremy Quastel, Timo Seppalainen

Research output: Contribution to journalArticle (Academic Journal)peer-review

59 Citations (Scopus)

Abstract

The KPZ equation is one of the central objects of statistical physics, and in
the recent years it also received great attention from mathematics part. The
equation being ill-posed, it is non trivial to talk about its solutions, and
interesting to deduce any properties of these solutions. Using a connection to
the weakly asymmetric simple exclusion process we could prove some scaling
properties of the (Hopf-Cole) solution of the KPZ equation.
Original languageEnglish
Article numberPII: S 0894-0347(2011)00692-9
Pages (from-to)683-708
Number of pages26
JournalJournal of the American Mathematical Society
Volume24
Issue number3
Early online date19 Jan 2011
DOIs
Publication statusPublished - Jul 2011

Keywords

  • Kardar-Parisi-Zhang equation
  • stochastic heat equation
  • stochastic Burgers equation
  • random growth
  • asymmetric exclusion process
  • anomalous fluctuations
  • directed polymers
  • RANDOM ENVIRONMENT
  • DIRECTED POLYMERS
  • SUPERDIFFUSIVITY

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