Asymptotic behaviors of the integrated density of states for random Schrödinger operators associated with Gibbs Point Processes

The asymptotic behaviors of the integrated density of states $N(\lambda )$ 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 $N(\lambda )$ as $\lambda \downarrow -\mathrm{\infty }$ 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 $N(\lambda )$ as $\lambda \downarrow -\mathrm{\infty }$ are determined, which are different from that for a Poisson point process.