2021/08/19 by Torben Krüger, Krüger, Torben, David Renfrew +1 · 1 citation
Mathematics · #Random Matrices and Applications #Advanced Algebra and Geometry #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2108.08811
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.