Limiting spectral distribution of a class of Hankel type random matrices

TL;DR

This paper investigates the spectral distribution limits of a broad class of Hankel-type random matrices, establishing almost sure convergence and continuity of the spectral distribution with respect to the matrix index.

Contribution

It introduces a generalized class of Hankel and Reverse Circulant matrices and proves the existence and continuity of their limiting spectral distributions.

Findings

Limiting spectral distributions exist almost surely.

Spectral distributions are continuous in the matrix index.

The results extend known spectral properties to a broader class of matrices.

Abstract

We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distributions of these matrices exist almost surely and the limit is continuous in the index. We also study other properties of the limit.