Test de normalité basé sur la caractéristique d'Euler des ensembles d'excursion

In the present talk, we deal with a stationary isotropic random field $X:\\R^d \\to \\R$ and we assume it is partially observed through some level functionals. We aim at providing a methodology for a test of Gaussianity based on this information. More precisely, the level functionals are given by the Euler characteristic of the excursion sets above some levels. On the one hand, we study the properties of these level functionals under the hypothesis that the random field $X$ is Gaussian. In particular, we focus on the mapping that associates to any $u$ the expected Euler characteristic of the excursion set above level $u$. On the other hand, we study the same level functionals under alternative distributions of $X$, such as chi-square or shot noise. The talk is based on a joint work with Elena Di Bernardino (CNAM Paris) and José R. Leon (Universidad Central de Venezuela).