Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket

Abstract

We establish the Lifschitz-type singularity around the bottom of the spectrum for the integrated density of states for a class of subordinate Brownian motions in presence of the nonnegative Poissonian random potentials, possibly of infinite range, on the Sierpiński gasket. We also study the long-time behaviour for the corresponding averaged Feynman-Kac functionals.

39 pages