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math.ST2026
Non-asymptotic Tail Bounds for the Kostlan--Shub--Smale Field: Tensor PCA and Spherical -Spin Complexity
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
This paper builds a hierarchy of explicit, non-asymptotic tail bounds for the supremum of the Kostlan--Shub--Smale (KSS) random field on the sphere, and applies it to two problems:…
math.ST2025
Second Maximum of a Gaussian Random Field and Exact (t-)Spacing test
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
In this article, we introduce the novel concept of the second maximum of a Gaussian random field on a Riemannian submanifold. This second maximum serves as a powerful tool for char…