The Asymptotic Equivalence of the Sample Trispectrum and the Nodal Length for Random Spherical Harmonics

Domenico Marinucci, Maurizia Rossi, Igor Wigman

We study the asymptotic behaviour of the nodal length of random $2d$-spherical harmonics $f_{\ell }$ of high degree $\ell \to \infty$, i.e. the length of their zero set $f_{\…