Suppose that a real valued stationary random field $X$ is observed through some of its excursion sets, ie {$t\in$ bounded rectangle $\subset {\Bbb R}^d$ : $X(t)\geq u$} for some levels $u$. We are interested in the following question : based on these observations (and no more), how can we validate or reject the fact that $X$ is Gaussian ? Actually, we focus on the distribution of the Euler characteristic of the excursion sets of $X$, under the hypothesis $X$ is Gaussian. We also provide 2D and 1D simulations that exhibit the specific behavior of the Gaussian case.

This is a work in progress with Elena Di Bernardino (CNAM) and José R. Leon (Universidad Central de Venezuela, INRIA Grenoble).

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