5 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:…
Landscape k-complexity of isotropic centered Gaussian fields
Jean-Marc Azaïs, Céline Delmas
In large dimension, we study the asymptotic behavior of the mean number of critical points with index k below a level u for an isotropic centered Gaussian random field defined on a…
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…
On a general Kac-Rice formula for the measure of a level set
Diego Armentano, Jean-Marc Azaïs, José Rafael León
Let be a random field , . We first studied the level set , . In particular we gave a weak condi…