On the Correlation of Critical Points and Angular Trispectrum for Random Spherical Harmonics

Abstract We prove a Central Limit Theorem for the critical points of random spherical harmonics, in high-energy limit. The result is consequence deeper characterization total number points, which are shown to be asymptotically fully correlated with sample trispectrum, i.e. integral fourth Hermite polynomial evaluated on eigenfunctions themselves. As consequence, and nodal length