Seminarium KMMF "Teoria Dwoistości"

I will present several results concerning the Lifschitz-tail asymptoticsfor operators of the form L=H+V, where H is a (possibly nonlocal) Levy operator and V is a random potential of either Poisson or lattice-type. We prove the existence of Lifschitz tail and establish theprecise rate of decay of the integrated density of states near thebottom of the spectrum.The results were obtained in collaboration with Kamil Kaleta (WroclawUniversity of Science and Technology).