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Strong Convergence for a General Class of Random Matrix Models — arXiv:2608.04824

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.04824
License (as archived): CC0-1.0
Archived: 2026-10-31T11:38:41.402Z
SHA-256 of the archived text: 8fc1a8f9e68e4e8da6d18c9909ad34bc6d5a5136453ddd09ecf7afd8f4ae1c7a
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Strong Convergence for a General Class of Random Matrix Models — arXiv:2608.04824 — arXiv (en), https://arxiv.org/abs/2608.04824 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9b64dcceea64 (Metraipolis archive dc_9b64dcceea64, sha256 8fc1a8f9e68e4e8da6d18c9909ad34bc6d5a5136453ddd09ecf7afd8f4ae1c7a)

BibTeX

@misc{dc9b64dcceea64,
  title = {Strong Convergence for a General Class of Random Matrix Models — arXiv:2608.04824},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.04824},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9b64dcceea64; sha256 8fc1a8f9e68e4e8da6d18c9909ad34bc6d5a5136453ddd09ecf7afd8f4ae1c7a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.04824. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let \(X_{1,n},\ldots,X_{d,n}\) be \(n\times n\) random matrices built from independent i.i.d. entry arrays, with centered entries, normalized by \(n^{-1/2}\). We prove that, if every entry law has finite fourth moment, then this tuple converges almost surely strongly in \(*\)-distribution to a free circular family with the matching variances. Equivalently, normalized traces and operator norms converge for every fixed noncommutative \(*\)-polynomial, including polynomials with fixed matrix coefficients. No assumption is imposed on the pseudo-variances of the complex entries. The bounded-entry argument applies the spectrum and moment universality estimates of Brailovskaya and van Handel to all self-adjoint linear pencils. The matching Gaussian pencils are reduced to independent Wigner matrices and identified by Anderson's strong convergence theorem. A fixed-level centered truncation, followed by the Bai--Yin norm bound, transfers the result to finite fourth moments.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-06 in math.ST).
Categorie arXiv: Probability (math.PR) ; Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2608.04824 — 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 2026-10-31T11:28:48.116Z dalla pagina https://arxiv.org/catchup/math.ST/2026-08-06?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).