Maximal and minimal height distributions of fluctuating interfaces

TL;DR

This paper investigates the statistical properties of maximum and minimum heights in fluctuating interfaces modeled by nonlinear growth equations, revealing universal behaviors and differences from classical distributions.

Contribution

It introduces a numerical analysis of MAHD and MIHD for nonlinear interface growth models, highlighting the role of nonlinear terms in determining distribution asymmetry and universality.

Findings

MAHD and MIHD differ due to local height distribution asymmetry.

Extreme height distributions have non-Gumbel tails.

Average extreme heights scale with the average roughness.

Abstract

We study numerically the maximal and minimal height distributions (MAHD, MIHD) of the nonlinear interface growth equations of second and fourth order and of related lattice models in two dimensions. MAHD and MIHD are different due to the asymmetry of the local height distribution, so that, in each class, the sign of the relevant nonlinear term determines which one of two universal curves is the MAHD and the MIHD. The average maximal and minimal heights scale as the average roughness, in contrast to Edwards-Wilkinson (EW) growth. All extreme height distributions, including the EW ones, have tails that cannot be fit by generalized Gumbel distributions.