Rank perturbations in random matrix theory -- a review of exact results

PJ Forrester - arXiv preprint arXiv:2201.00324, 2022 - arxiv.org
A number of random matrix ensembles permitting exact determination of their eigenvalue
and eigenvector statistics maintain this property under a rank $1 $ perturbation. Considered …

[HTML][HTML] A generalized Hermite–Biehler theorem and non-Hermitian perturbations of Jacobi matrices

R Kozhan, M Tyaglov - Journal of Mathematical Analysis and Applications, 2024 - Elsevier
Abstract The classical Hermite–Biehler theorem describes the zero configuration of a
complex linear combination of two real polynomials whose zeros are real, simple, and …

Multiplicative non-Hermitian perturbations of classical -ensembles

G Alpan, R Kozhan - arXiv preprint arXiv:2308.06627, 2023 - arxiv.org
arXiv:2308.06627v1 [math.PR] 12 Aug 2023 Page 1 arXiv:2308.06627v1 [math.PR] 12 Aug
2023 MULTIPLICATIVE NON-HERMITIAN PERTURBATIONS OF CLASSICAL β-ENSEMBLES …

A generalized Hermite-Biehler theorem

R Kozhan, M Tyaglov - arXiv preprint arXiv:2302.07018, 2023 - arxiv.org
The classical Hermite-Biehler theorem describes possible zero sets of complex linear
combinations of two real polynomials whose zeros strictly interlace. We provide the full …