The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion

TL;DR

This paper presents numerical evidence that challenges the assumption that the Airy_1 process describes the limiting behavior of the largest eigenvalue in GOE matrix diffusion, a key question in random matrix theory.

Contribution

The authors provide the first systematic numerical analysis indicating that the Airy_1 process is not the limit law for GOE matrix diffusion's largest eigenvalue.

Findings

Numerical evaluation of Fredholm determinants shows deviation from Airy_1 process.

Evidence suggests the limit law differs from the Airy_1 process in GOE diffusion.

Challenges previous conjectures linking Airy_1 to GOE eigenvalue limits.

Abstract

Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy_1-process, arising as a limit law in stochastic surface growth, is not the limit law for the evolution of the largest eigenvalue in GOE matrix diffusion.