Number of critical points of a Gaussian random field: Condition for a finite variance

Anne Estrade (1) , Julie Fournier (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We study the number of points where the gradient of a stationary Gaussian random field restricted to a compact set in $\mathbb{R}^d$ takes a fixed value. We extend to higher dimensions the Geman condition, a sufficient condition on the covariance function under which the variance of this random variable is finite.

Mots clés: Gaussian field; Critical point; Geman condition; Crossing

Domaines: Mathématiques [math]

Anne Estrade, Julie Fournier. Number of critical points of a Gaussian random field: Condition for a finite variance. Statistics and Probability Letters, 2016, 118, pp.94-99. ⟨10.1016/j.spl.2016.06.018⟩. ⟨hal-01374125⟩