4 papers
Multivariable CLT for critical points
Jean-Marc Azaïs, Federico Dalmao, Céline Delmas
We prove a multivariate central limit theorem for the numbers of critical points with all possible indexes which lie above a level of a non-necessarily isotropic Gaussian random fi…
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:…
Gaussian random field's anisotropy using excursion sets
Jean-Marc Azaïs, Federico Dalmao, Yohann De Castro
This paper addresses the problem of detecting and estimating the anisotropy of a stationary real-valued random field from a single realization of one of its excursion sets. This se…
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…