Random waves on ${\mathbb{T}}^3$: nodal area variance and lattice point correlations

Jacques Benatar, Riccardo W. Maffucci

We consider the ensemble of random Gaussian Laplace eigenfunctions on ${\mathbb{T}}^3={\mathbb{R}}^3/{\mathbb{Z}}^3$ (`$3d$ arithmetic random waves'), and study the distribution of their…