Eigenvalue statistics for Schrödinger operators with random point interactions on R d, d = 1, 2, 3

We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on Rd, 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 Schrödinger operators in the continuum. The special structure of resolvent of Schrödinger operators with point interactions facilitates the proof of the Minami estimate for these models.