One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes

[2608.15137] One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2608.15137 (math) [Submitted on 15 Aug 2026] Title: One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes Authors: Xiufan Yang View a PDF of the paper titled One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes, by Xiufan Yang View PDF HTML (experimental) Abstract: 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. Comments: 92 pages Subjects: Probability (math.PR) ; Spectral Theory (math.SP) MSC classes: Primary 60B20, Secondary 60F15, 60G55 Cite as: arXiv:2608.15137 [math.PR] (or arXiv:2608.15137v1 [math.PR] for this version) https://doi.org/10.48550/arXiv.2608.15137 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xiufan Yang [ view email ] [v1] Sat, 15 Aug 2026 09:20:58 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes, by Xiufan Yang View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-08 Change to browse by: math math.SP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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