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

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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Correspondence to Nicolas Perkowski.

Additional information

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.

Communicated by H. Spohn

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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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