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Communications in Mathematical Physics

, Volume 354, Issue 2, pp 549–589 | Cite as

The Kardar–Parisi–Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions

  • Joscha Diehl
  • Massimiliano Gubinelli
  • Nicolas PerkowskiEmail author
Article

Abstract

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove that the large scale fluctuations of the system are well approximated by the solution to the KPZ equation provided the microscopic interaction is weakly asymmetric. The proof is based on the martingale solutions of Gonçalves and Jara (Arch Ration Mech Anal 212(2):597–644, 2014) and the corresponding uniqueness result of Gubinelli and Perkowski (Energy solutions of KPZ are unique, 2015).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Hausdorff Center for Mathematics and Institute for Applied Mathematics UniversitätBonnGermany
  3. 3.Institut für MathematikHumboldt–Universität zuBerlinGermany

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