Singularity degree of structured random matrices

Torben Krüger; David Renfrew

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arXiv · 2108.08811

Singularity degree of structured random matrices

Torben Krüger·David Renfrew

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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.

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BibTeX RIS

Torben Krüger, David Renfrew. 2021-08-19. Singularity degree of structured random matrices. https://arxiv.org/abs/2108.08811

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