Current browse context:
math.PR
Change to browse by:
References & Citations
Mathematics > Probability
Title: Spectrum occupies pseudospectrum for random matrices with diagonal deformation and variance profile
(Submitted on 26 Apr 2024)
Abstract: We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that the support of the asymptotic eigenvalue distribution in the complex plane exactly coincides with the $\varepsilon$-pseudospectrum in the consecutive limits $n \to \infty$ and $\varepsilon \to 0$. Furthermore, we provide a description of this support in terms of a single real-valued function on the complex plane. As a level set of this locally real analytic function, the spectral edge is a real analytic variety of dimension at most one.
Link back to: arXiv, form interface, contact.