Singularity degree of structured random matrices
Abstract
We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up, which we label the singularity degree.
Cite
@article{arxiv.2108.08811,
title = {Singularity degree of structured random matrices},
author = {Torben Krüger and David Renfrew},
journal= {arXiv preprint arXiv:2108.08811},
year = {2024}
}
Comments
In the technical Section 5 of the published version of this work, Definition 5.3 (Boundary condition) omits a monotonicity requirement that takes the edges of the surrounding graph into account. We amended Definition 5.3 with this monotonicity condition in this latest arXiv-version. This monotonicity requirement had been tacitly assumed in the proofs, so all theorems and proofs remain unchanged