A class of growth models rescaling to KPZ

TL;DR

This paper demonstrates that a broad class of 1+1-dimensional continuous interface growth models converge to the KPZ equation's solutions under specific regimes, unifying various models within a common theoretical framework.

Contribution

It establishes convergence of diverse growth models to the KPZ equation in both weakly asymmetric and intermediate disorder regimes, extending the universality class understanding.

Findings

Models converge to KPZ solutions in specified regimes

Unification of growth models under KPZ universality

Provides rigorous mathematical proof of convergence

Abstract

We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.