  We define a random model for the moments of the new eigenfunctions of a point
scat-terer on a 2-dimensional rectangular flat torus. In the deterministic
setting,Seba conjectured these moments to be asymptotically Gaussian, in the
semi-classical limit. This conjecture was disproved by Kurlberg-Uebersch{\"a}r
on Diophantine tori. In our model, we describe the accumulation points in
distribution of the randomized moments, in the semi-classical limit. We prove
that asymptotic Gaussianity holds if and only if some function, modeling the
multiplicities of the Laplace eigenfunctions, diverges to +$\infty$.
