Location of the spectrum of Kronecker random matrices

Johannes Alt; Laszlo Erdos; Torben Krüger; Yuriy Nemish

Location of the spectrum of Kronecker random matrices

Probability 2018-02-27 v3 Mathematical Physics math.MP

Authors: Johannes Alt , Laszlo Erdos , Torben Krüger , Yuriy Nemish

Abstract

For a general class of large non-Hermitian random block matrices $\mathbf{X}$ we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of $\mathbf{X}$ as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from [arXiv:1604.08188v4] offers a unified treatment of many structured matrix ensembles.

Keywords

kronecker random matrices non-hermitian random block matrices dyson equation hermitization pseudospectrum eigenvalue location matrix ensembles

Cite

@article{arxiv.1706.08343,
  title  = {Location of the spectrum of Kronecker random matrices},
  author = {Johannes Alt and Laszlo Erdos and Torben Krüger and Yuriy Nemish},
  journal= {arXiv preprint arXiv:1706.08343},
  year   = {2018}
}

Comments

33 pages, 4 figures. Some assumptions in Section 3.1 and 3.2 relaxed. Some typos corrected and references updated

Location of the spectrum of Kronecker random matrices

Abstract

Keywords

Cite

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