Location of the spectrum of Kronecker random matrices

2017/06/26 by Johannes Alt, Alt, Johannes, Laszlo Erdos +5 · 3 citations
Mathematics · Physics and Astronomy · #15B52 #60B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:15B52 #msc:60B20

paper · pdf · doi:10.48550/arxiv.1706.08343

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

arxiv created 2018/02/25 · arxiv updated 2018/02/27

Abstract

For a general class of large non-Hermitian random block matrices 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 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.

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