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

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