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Tracy Widom law for sample covariance matrices under quadratic form concentration — arXiv:2610.41416

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41416
License (as archived): CC0-1.0
Archived: 2026-11-03T05:43:28.040Z
SHA-256 of the archived text: 4c04c1f5f42db52127982056e8503b4153542fd002392f4335d5c5ef5dfab79a
Stable URL of this page: https://metraipolis.com/documento/dc_dadfe4407fa5

How to cite

Tracy Widom law for sample covariance matrices under quadratic form concentration — arXiv:2610.41416 — arXiv (en), https://arxiv.org/abs/2610.41416 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_dadfe4407fa5 (Metraipolis archive dc_dadfe4407fa5, sha256 4c04c1f5f42db52127982056e8503b4153542fd002392f4335d5c5ef5dfab79a)

BibTeX

@misc{dcdadfe4407fa5,
  title = {Tracy Widom law for sample covariance matrices under quadratic form concentration — arXiv:2610.41416},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41416},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_dadfe4407fa5; sha256 4c04c1f5f42db52127982056e8503b4153542fd002392f4335d5c5ef5dfab79a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41416. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study sample covariance matrices formed from i.i.d., centered, isotropic random vectors $q_1, \dots, q_N \in \mathbb{R}^M$, whose coordinates are allowed to be dependent. We assume the random vectors satisfy a concentration bound for their quadratic forms $q_i^T A q_i$. Under this assumption, we establish edge universality and obtain the Tracy--Widom law for the largest eigenvalue of the sample covariance matrix after appropriate centering and scaling. In particular, our result removes the unconditionality assumption in existing edge universality results for log-concave ensembles~\cite{BX}, resolving the question that originally motivated our work. The concentration assumption also allows us to extend the result beyond the log-concave class.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Mathematical Physics (math-ph); Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2610.41416 — 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 2026-11-03T05:31:31.300Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).