# Spectral Convergence of Large Block-Hankel Gaussian Random Matrices

## TL;DR

This paper analyzes the spectral behavior of large block-Hankel Gaussian random matrices, showing that their empirical eigenvalue distribution converges to a deterministic limit as matrix dimensions grow infinitely large.

## Contribution

It provides a rigorous characterization of the eigenvalue distribution convergence for large block-Hankel Gaussian matrices using the Stieltjes transform approach.

## Key findings

- Empirical eigenvalue distribution converges to a deterministic limit.
- The limit is characterized explicitly in the asymptotic regime.
- The results apply when matrix dimensions grow proportionally.

## Abstract

This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from complex Gaussian correlated stationary random sequences. In the asymptotic regime where M \rightarrow \infty, N \rightarrow +\infty and ML/N \rightarrow c > 0, it is shown using the Stieltjes transform approach that the empirical eigenvalue distribution of W_N W_N* has a deterministic behaviour which is characterized.