On the limiting behaviour of arithmetic toral eigenfunctions

Riccardo W. Maffucci, Alejandro Rivera

We consider a wide class of families $(F_m{)}_{m\in \mathbb{N}}$ of Gaussian fields on ${\mathbb{T}}^d={\mathbb{R}}^d/{\mathbb{Z}}^d$ defined by \[F_m:x\mapsto \frac{1}{\sqrt{|Λ_m|}}\sum_{λ…