Limiting Spectral Distributions of Families of Block Matrix Ensembles

Authors

  • Teresa Dunn University of California, Davis
  • Henry L. Fleischmann University of Michigan
  • Faye Jackson University of Michigan
  • Simran Khunger Carnegie Mellon University
  • Steven J. Miller Williams College
  • Luke Reifenberg University of Notre Dame
  • Alexander Shashkov Williams College
  • Stephen Willis Williams College

DOI:

https://doi.org/10.46787/pump.v5i0.2880

Keywords:

random matrix theory; block matrices; Rayleigh distribution; method of moments; Hankel matrices

Abstract

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.

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Published

2022-06-08

How to Cite

Dunn, T., Fleischmann, H., Jackson, F., Khunger, S., Miller, S., Reifenberg, L., … Willis, S. (2022). Limiting Spectral Distributions of Families of Block Matrix Ensembles. The PUMP Journal of Undergraduate Research, 5, 122–147. https://doi.org/10.46787/pump.v5i0.2880