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One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes — arXiv:2608.15137

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.15137
License (as archived): CC0-1.0
Archived: 2026-10-18T20:24:58.822Z
SHA-256 of the archived text: 5933f540d2c078f6492bf81edcea8457996c6fc098a9eef9dfc956cdb304d142
Stable URL of this page: https://metraipolis.com/documento/dc_7485e421ee84

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One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes — arXiv:2608.15137 — arXiv (en), https://arxiv.org/abs/2608.15137 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7485e421ee84 (Metraipolis archive dc_7485e421ee84, sha256 5933f540d2c078f6492bf81edcea8457996c6fc098a9eef9dfc956cdb304d142)

BibTeX

@misc{dc7485e421ee84,
  title = {One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes — arXiv:2608.15137},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.15137},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7485e421ee84; sha256 5933f540d2c078f6492bf81edcea8457996c6fc098a9eef9dfc956cdb304d142},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.15137. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

I study the largest eigenvalue \(\Lambda_j\) of \(X^{(j)}(X^{(j)})^*\), where \(X^{(j)}\) is the \(M_j\times j\) northwest rectangle of one infinite complex Gaussian array. For two upper-tail events and, separately, for two lower-tail events at the largest-eigenvalue soft edge, I prove finite-\(N\) one-sided product-scale upper bounds for their joint probabilities. The logarithmic walls have polynomially small marginals, so an additive \(o(1)\) covariance estimate may be much larger than the vanishing product that must be controlled. Uniformly for levels in a short macroscopic window, bounded deterministic shifts, and separations at least \(N^{2/3+\epsilon}\), each joint probability is at most \((1+o(1))\) times the product of its marginals. The classical \(N^{2/3}\) correlation window corresponds to order-one extended-Airy time; the theorem works at supercritical separation. Exact Laguerre operators along admissible row--column paths provide the finite-dimensional input. The upper-tail proof uses occupancy counts and cross-block trace estimates, whereas the lower-tail proof uses gap determinants, diagonal resolvents, and a Schur complement. I transfer the result between the half-integer Laguerre and physical rectangular normalizations and deduce intrinsic first- and second-moment estimates for separated sparse grids under the rarity, count-growth, spacing, and macroscopic-window budget.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-18 in math.PR).
Categorie arXiv: Probability (math.PR) ; Spectral Theory (math.SP).
Pagina del lavoro: https://arxiv.org/abs/2608.15137 — 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 2026-10-18T19:45:36.370Z dalla pagina https://arxiv.org/catchup/math.PR/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).