Parametric level statistics in random matrix theory: Exact solution

TL;DR

This paper provides an exact solution for parametric level statistics in non-Gaussian Hermitian random matrix ensembles, revealing new connections between level statistics and two-point kernels in the thermodynamic limit.

Contribution

It introduces an exact analytical approach using orthogonal polynomials for non-Gaussian ensembles with strong confinement, establishing a novel link to two-point kernels.

Findings

Exact solution for parametric level statistics in non-Gaussian ensembles

Discovery of a new connection relation in the thermodynamic limit

Application to ensembles with strong level confinement

Abstract

An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of N by N Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial technique. Being applied to random matrices with strong level confinement, the solution obtained leads to emergence of a new connection relation that makes a link between the parametric level statistics and the scalar two-point kernel in the thermodynamic limit.