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Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices

  • Pierre Bousseyroux
  • Marc Potters
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Abstract

We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form A(I+T), where A is a large rotationally invariant non-Hermitian random matrix, T is a finite-rank normal perturbation, and I denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--Péché framework.

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Cite

BibTeXRIS
BibTeX
@misc{bousseyroux2026finiterank,
  title = {{Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices}},
  author = {Pierre Bousseyroux and Marc Potters},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07220},
  eprint = {2609.07220},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07220},
}
RIS
TY  - UNPB
TI  - Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices
AU  - Pierre Bousseyroux
AU  - Marc Potters
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.07220
UR  - https://arxiv.org/abs/2609.07220
AB  - We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form A(I+T), where A is a large rotationally invariant non-Hermitian random matrix, T is a finite-rank normal perturbation, and I denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--Péché framework.
ER  -