Integrated density of states for the Poisson point interactions on R³

We determine the principal term of the asymptotics of the integrated density of states (IDS) N(λ) for the Schr\"odinger operator with point interactions on R³ as λ → -∞, 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→ -∞. 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.