Random anti-commuting Hermitian matrices
Probability
2023-12-25 v1
Abstract
We consider pairs of anti-commuting -by- Hermitian matrices that are chosen randomly with respect to a Gaussian measure. Generically such a pair decomposes into the direct sum of -by- blocks on which the first matrix has eigenvalues and the second has eigenvalues . We call the skew spectrum of the pair. We derive a formula for the probability density of the skew spectrum, and show that the elements are repelling.
Cite
@article{arxiv.2312.14330,
title = {Random anti-commuting Hermitian matrices},
author = {John E. McCarthy and Hazel T. McCarthy},
journal= {arXiv preprint arXiv:2312.14330},
year = {2023}
}