Asymptotic Behaviour of Linear eigenvalue statistics of Hankel matrices

TL;DR

This paper investigates the asymptotic distribution of linear eigenvalue statistics of band Hankel matrices with Brownian motion entries, establishing a CLT and discussing convergence for matrices with independent entries.

Contribution

It introduces a CLT for linear eigenvalue statistics of band Hankel matrices with Brownian motion entries and analyzes convergence for matrices with independent entries.

Findings

Centered, normalized eigenvalue statistics follow a CLT.

Convergence results for matrices with independent entries and odd power monomials.

Method combines trace formula, moment method, and process convergence.

Abstract

We study linear eigenvalue statistics of band Hankel matrices with Brownian motion entries. We prove that, the centred, normalized linear eigenvalue statistics of band Hankel matrices obey a central limit theorem (CLT) type result. We also discuss the convergence of linear eigenvalue statistics of band Hankel matrices with independent entries for odd power monomials. Our method is based on trace formula, moment method and some results of process convergence.