We prove that the local eigenvalue statistics for Schrödinger operators with random point interactions on $\mathbb R^d$, for $d=1,2,3$ is Poissonian in the localization regime. This is the first example of eigenvalue statistics for multi-dimensional random Schrödinger operators in the continuum.
The special structure of the point interactions facilitates the proof of the Minami estimate.
This is joint work with W. Kirsch and M. Krishna.