Asymptotic behaviors of the integrated density of states for random Schr\"odinger operators associated with Gibbs Point Processes

Abstract

The asymptotic behaviors of the integrated density of states $N(\lambda)$ of Schr\"odinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading terms of $N(\lambda)$ as $\lambda\downarrow-\infty$ 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 $N(\lambda)$ as $\lambda\downarrow-\infty$ are determined, which are different from that for a Poisson point process.