The limiting spectral distribution of the generalized Wigner matrix

TL;DR

This paper investigates the limiting spectral distribution of generalized Wigner matrices and applies the findings to analyze the energy of general random graphs, extending previous results in spectral theory.

Contribution

It extends the understanding of spectral distributions from classical Wigner matrices to more general random matrices and applies this to graph energy analysis.

Findings

Established the limiting spectral distribution for generalized Wigner matrices

Connected spectral properties to the energy of random graphs

Generalized previous results by Nikiforov

Abstract

The properties of eigenvalues of large dimensional random matrices have received considerable attention. One important achievement is the existence and identification of the limiting spectral distribution of the empirical spectral distribution of eigenvalues of Wigner matrix. In the present paper, we explore the limiting spectral distribution for more general random matrices, and, furthermore, give an application to the energy of general random graphs, which generalizes the result of Nikiforov.