Random commuting matrices
Probability
2025-05-15 v2 Functional Analysis
Abstract
We define a random commuting -tuple of -by- matrices to be a random variable that takes values in the set of commuting -tuples and has a distribution that is a rapidly decaying continuous weight on this algebraic set. In the Hermitian case, we characterize the eigenvalue distribution as tends to infinity. In the non-Hermitian case, we get a formula that holds if the set is irreducible. We show that there are qualitative differences between the single matrix case and the several commuting matrices case.
Cite
@article{arxiv.2305.20029,
title = {Random commuting matrices},
author = {John E. McCarthy},
journal= {arXiv preprint arXiv:2305.20029},
year = {2025}
}