Limiting Spectral Distributions of Families of Block Matrix Ensembles - Dunn, Teresa; Fleischmann, Henry; Jackson, Faye; Khunger, Simran; Miller, Steven; Reifenberg, Luke; Shashkov, Alexander; Willis, Stephen (The PUMP Journal of Undergraduate Research, 2022)
We introduce a new matrix operation on a pair of matrices, sw(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.