Spectrum of Random Matrices with Exploding Moments

TL;DR

This paper investigates the CLT for eigenvalue statistics of various matrix models with entries whose moments grow with matrix size, using asymptotic Wick formula.

Contribution

It extends CLT results to matrix models with exploding moments, including elliptic, centrosymmetric, circulant, and inter-correlated block matrices.

Findings

Established CLTs for eigenvalue statistics in models with exploding moments

Applied asymptotic Wick formula to derive results

Analyzed multiple matrix types with growing entry moments

Abstract

We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular, we study elliptic, centrosymmetric, circulant, and inter-correlated block matrices. The CLTs are established using asymptotic Wick formula.