Integrated density of states for the Poisson point interactions on $\mathbf{R}^3$

We determine the principal term of the asymptotics of the integrated density of states (IDS) $N(λ)$ for the Schrödinger operator with point interactions on $\mathbf{R}^3$ as $λ\to -\infty$, provided that the set of positions of the point obstacles is the Poisson configuration, and the interaction parameters are bounded i.i.d.\ random variables. In particular, we prove $N(λ) =O(|λ|^{-3/2})$ as $λ\to -\infty$. In the case that all interaction parameters are equal to a constant, we give a more detailed asymptotics of $N(λ)$, and verify the result by a numerical method using R.