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Spike Irrelevance and Convergence Rate at the Non-Hermitian BBP Transition — arXiv:2609.19221

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.19221
License (as archived): CC0-1.0
Archived: 2026-10-10T04:23:33.565Z
SHA-256 of the archived text: 1a6575b159e7bd1f39617a873e4259d7888788560324201d75977a6f3a7318c2
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How to cite

Spike Irrelevance and Convergence Rate at the Non-Hermitian BBP Transition — arXiv:2609.19221 — arXiv (en), https://arxiv.org/abs/2609.19221 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b01c19ca5bb3 (Metraipolis archive dc_b01c19ca5bb3, sha256 1a6575b159e7bd1f39617a873e4259d7888788560324201d75977a6f3a7318c2)

BibTeX

@misc{dcb01c19ca5bb3,
  title = {Spike Irrelevance and Convergence Rate at the Non-Hermitian BBP Transition — arXiv:2609.19221},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.19221},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b01c19ca5bb3; sha256 1a6575b159e7bd1f39617a873e4259d7888788560324201d75977a6f3a7318c2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.19221. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study a rank-one spiked complex Ginibre ensemble A_N = X_N + sigma u u^*, where X_N is an N by N complex Ginibre matrix with independent entries distributed as CN(0,1/N), u is a deterministic unit vector, and sigma is a nonnegative spike strength. We focus on the maximum real part of the eigenvalues and its behavior near the non-Hermitian BBP transition. For every fixed subcritical spike strength sigma < 1, we show that the maximum real part has the same Gumbel limit as in the unspiked ensemble, after the same centering and scaling. We also derive an explicit convergence-rate correction of order 1/log N for the unspiked Gumbel law. At the critical point sigma = 1, we establish an upper bound for the rightmost eigenvalue at the N^{-1/4} scale using isotropic resolvent estimates and a net argument.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-18 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.19221 — 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 2026-10-10T04:09:58.334Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).