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

The asymptotic behaviors of the integrated density of states N(lambda) of Schrodinger 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 down arrow -infinity 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 down arrow -infinity are determined, which are different from that for a Poisson point process.