Eigenvalue statistics for Schr\"odinger operators with random point interactions on ${\mathbb{R}}^d$, $d=1,2,3$

We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schr"odinger operators with random point interactions on ${\mathbb{R}}^d$, for $d=1,2,3$, is a Poisson point process with the intensity measure given by the density of states at $E$ times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schr"odinger operators in the continuum. The special structure of resolvent of Schr"odinger operators with point interactions facilitates the proof of the Minami estimate for these models.