J. Azais

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math.PR2026

Multivariable CLT for critical points

Jean-Marc AzaÃ¯s, Federico Dalmao, CÃ©line 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…

math.PR2026

Landscape k-complexity of isotropic centered Gaussian fields

Jean-Marc AzaÃ¯s, CÃ©line 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…

math.PR2025

On a general Kac-Rice formula for the measure of a level set

Let $X (\cdot)$ be a random field $R^{D} \to R^{d}$ , $D \geq d$ . We first studied the level set $X^{- 1} (u)$ , $u \in R^{d}$ . In particular we gave a weak condi…