Asymptotic behaviour of level sets of needlet random fields

We consider sequences of needlet random fields defined as weighted averaged forms spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for boundary lengths their excursion sets. This based on Wiener chaos expansion and Stein–Malliavin techniques nonlinear functionals fields. To this end, careful analysis variances each chaotic component length carried out, showing that they are asymptotically constant, after normalisation, all terms no leading arises.