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Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles

  • Pierre Bousseyroux
  • Marc Potters
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Abstract

In this paper, we study spectral properties of multiplicative deformations of non-Hermitian random matrices. We consider matrices of the form AB, where A is a deterministic N× N matrix (not necessarily Hermitian) and B is a rotationally invariant random matrix. We show that, as N→∞, the boundary of the complex eigenvalue distribution of AB is governed by simple equations involving the ℛ1 and ℛ2 transforms of B.

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Cite

BibTeXRIS
BibTeX
@misc{bousseyroux2026spectral,
  title = {{Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles}},
  author = {Pierre Bousseyroux and Marc Potters},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03618},
  eprint = {2609.03618},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03618},
}
RIS
TY  - UNPB
TI  - Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles
AU  - Pierre Bousseyroux
AU  - Marc Potters
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03618
UR  - https://arxiv.org/abs/2609.03618
AB  - In this paper, we study spectral properties of multiplicative deformations of non-Hermitian random matrices. We consider matrices of the form AB, where A is a deterministic N× N matrix (not necessarily Hermitian) and B is a rotationally invariant random matrix. We show that, as N→∞, the boundary of the complex eigenvalue distribution of AB is governed by simple equations involving the ℛ_1 and ℛ_2 transforms of B.
ER  -