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

Journal of Mathematical Physics, Volume 61, Issue 9, September 2020. We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on [math], 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.