Limiting Spectral Distributions of Families of Block Matrix Ensembles

Teresa Dunn, Henry L. Fleischmann, Faye Jackson, Simran Khunger, Steven J. Miller, Luke Reifenberg, Alexander Shashkov, Stephen Willis

Published 2021-09-03Version 1

We introduce a new matrix operation on a pair of matrices, $\text{swirl}(A,X),$ and discuss its implications on the limiting spectral distribution. In a special case, the resultant ensemble converges almost surely to the Rayleigh distribution. In proving this, we provide a novel combinatorial proof that the random matrix ensemble of circulant Hankel matrices converges almost surely to the Rayleigh distribution, using the method of moments.