Asymptotic behaviors of the integrated density of states for random Schrödinger operators associated with Gibbs point processes

Abstract

The asymptotic behaviors of the integrated density of states $N(\mathit{\lambda })$ of Schrödinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading terms of $N(\mathit{\lambda })$ as $\mathit{\lambda }\downarrow -\mathrm{\infty }$ coincide with that for a Poisson point process, which is known. Moreover, for some Gibbs point processes corresponding to pairwise interactions, the leading terms of $N(\mathit{\lambda })$ as $\mathit{\lambda }\downarrow -\mathrm{\infty }$ are determined, which are different from that for a Poisson point process.