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

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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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Author information

Authors and Affiliations

  1. Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Joscha Diehl

  2. Hausdorff Center for Mathematics and Institute for Applied Mathematics Universität, Bonn, Germany

    Massimiliano Gubinelli

  3. Institut für Mathematik, Humboldt–Universität zu, Berlin, Germany

    Nicolas Perkowski

Authors
  1. Joscha Diehl
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  2. Massimiliano Gubinelli
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  3. Nicolas Perkowski
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Corresponding author

Correspondence to Nicolas Perkowski.

Additional information

Communicated by H. Spohn

J. Diehl: Finanical support by the DAAD P.R.I.M.E. program is gratefully acknowledged.

N. Perkowski: Financial support by the DFG via Research Unit FOR 2402 is gratefully acknowledged.

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Diehl, J., Gubinelli, M. & Perkowski, N. The Kardar–Parisi–Zhang Equation as Scaling Limit of Weakly Asymmetric Interacting Brownian Motions. Commun. Math. Phys. 354, 549–589 (2017). https://doi.org/10.1007/s00220-017-2918-6

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  • DOI: https://doi.org/10.1007/s00220-017-2918-6

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