Mean number and correlation function of critical points of isotropic Gaussian fields and some results on GOE random matrices

Jean-Marc Azais, Céline Delmas

Let $\mathcal{X}=\{X(t):t\in {\mathbb{R}}^N\}$ be an isotropic Gaussian random field with real values.In a first part we study the mean number of critical points of $\mathcal{X…