Rescaling Ward identities in the random normal matrix model

TL;DR

This paper investigates the behavior and universal properties of eigenvalues in random normal matrices, especially near the spectrum boundary, using Ward's equation to analyze the 1-point function.

Contribution

It introduces a novel approach employing Ward's equation to study eigenvalue scaling limits and universality in the random normal matrix model.

Findings

Establishes existence of scaling limits at spectrum boundary

Demonstrates universality of eigenvalue distributions

Provides new insights into Ward's equation in this context

Abstract

We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's equation, which is an identity satisfied by the 1-point function.