Fluctuations of eigenvalues of random normal matrices

TL;DR

This paper proves that the fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet converge to a Gaussian field, providing insight into their statistical behavior.

Contribution

It establishes Gaussian field convergence of eigenvalue fluctuations for random normal matrices, a novel result in the study of quantum droplet models.

Findings

Eigenvalue fluctuations converge to a Gaussian field

Results apply to the interior of quantum droplets

Advances understanding of eigenvalue statistics in random matrices

Abstract

In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.