Universal fluctuations in radial growth models belonging to the KPZ universality class

TL;DR

This study confirms that the radius distributions of radial growth models in the KPZ universality class follow the Tracy-Widom distribution, supporting the universality conjecture through large-scale simulations and correlation analysis.

Contribution

It provides the first comprehensive numerical verification that all investigated KPZ radial models exhibit Tracy-Widom distributions, completing the conjecture's validation.

Findings

Radius distributions match Tracy-Widom distribution

Two-point correlations align with Airy$_2$ process covariance

Results fill the last gap in KPZ universality conjecture

Abstract

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of the Gaussian unitary ensemble, in agreement with the conjecture of the KPZ universality class for curved surfaces. The quantitative agreement was also confirmed by two-point correlation functions asymptotically given by the covariance of the Airy$_2$ process. Our simulation results fill the last lacking gap of the conjecture that had been recently verified analytically and experimentally.