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Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles — arXiv:2609.03618

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03618
License (as archived): CC0-1.0
Archived: 2026-10-17T02:32:25.509Z
SHA-256 of the archived text: d1790b644e8809504b691bc66d67bef7c49b094d0de497c68edce2f9ad136e66
Stable URL of this page: https://metraipolis.com/documento/dc_14005bcdffe2

How to cite

Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles — arXiv:2609.03618 — arXiv (en), https://arxiv.org/abs/2609.03618 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_14005bcdffe2 (Metraipolis archive dc_14005bcdffe2, sha256 d1790b644e8809504b691bc66d67bef7c49b094d0de497c68edce2f9ad136e66)

BibTeX

@misc{dc14005bcdffe2,
  title = {Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles — arXiv:2609.03618},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03618},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_14005bcdffe2; sha256 d1790b644e8809504b691bc66d67bef7c49b094d0de497c68edce2f9ad136e66},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03618. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we study spectral properties of multiplicative deformations of non-Hermitian random matrices. We consider matrices of the form $\mathbf{A}\mathbf{B}$, where $\mathbf{A}$ is a deterministic $N\times N$ matrix (not necessarily Hermitian) and $\mathbf{B}$ is a rotationally invariant random matrix. We show that, as $N\to\infty$, the boundary of the complex eigenvalue distribution of $\mathbf{A}\mathbf{B}$ is governed by simple equations involving the $\mathcal{R}_1$ and $\mathcal{R}_2$ transforms of $\mathbf{B}$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-04 in math.PR).
Categorie arXiv: Disordered Systems and Neural Networks (cond-mat.dis-nn) ; Mathematical Physics (math-ph); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.03618 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:08:47.881Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).