What is the connection between ballistic deposition and the Kardar-Parisi-Zhang equation?

TL;DR

This paper critically examines the assumed link between ballistic deposition and the KPZ equation, deriving a continuum model from BD rules that differs from KPZ, especially in higher dimensions or deterministic cases.

Contribution

It provides a rigorous derivation showing that the continuum limit of BD deviates from the KPZ equation, challenging the universality assumption.

Findings

Deviations from KPZ are negligible in 1D with noise

Differences become significant in higher dimensions

Deterministic evolution of BD differs from KPZ predictions

Abstract

Ballistic deposition (BD) is considered to be a paradigmatic discrete growth model that represents the Kardar-Parisi-Zhang (KPZ) universality class. In this paper we question this connection by rigorously deriving a formal continuum equation from the BD microscopic rules, which deviates from the KPZ equation. In one dimension these deviations are not important in the presence of noise, but for higher dimensions or when considering deterministic evolution they are very relevant.