The Kardar-Parisi-Zhang equation as scaling limit of weakly asymmetric   interacting Brownian motions
  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 Goncalves and Jara and the corresponding uniqueness result of Gubinelli and Perkowski. 
Joscha Diehl and Massimiliano Gubinelli and Nicolas Perkowski
math.PR math-ph math.AP math.MP