Microscopic derivation of Kardar-Parisi-Zhang Equation

TL;DR

This paper rigorously derives the Kardar-Parisi-Zhang equation as the scaling limit of a one-dimensional weakly asymmetric growth model, providing a microscopic foundation for this fundamental stochastic PDE.

Contribution

It offers a microscopic derivation of the KPZ equation from a specific random growth process, connecting discrete models to continuous stochastic PDEs.

Findings

Fluctuation field converges to KPZ equation in the scaling limit

Establishes a rigorous link between microscopic growth models and KPZ universality

Demonstrates the universality class of the model in one dimension

Abstract

We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the Kardar-Parisi-Zhang equation.