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

arXiv · 2109.01464

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

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Abstract

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.

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Teresa Dunn, Henry L. Fleischmann, Faye Jackson, Simran Khunger, Steven J. Miller, Luke Reifenberg, Alexander Shashkov, Stephen Willis. 2021-09-03. Limiting Spectral Distributions of Families of Block Matrix Ensembles. https://arxiv.org/abs/2109.01464

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