The Lifschitz singularity for the density of states on the Sierpinski gasket (Q756291)

We prove the existence of the density of states for the Laplacian on the infinite Sierpinski gasket. Then the Lipschitz-type singularity of the density of states is established. We also investigate the long-time asymptotics of the Brownian trajectory on the Sierpinski gasket, getting bounds similar to those in the \({\mathbb{R}}^ d\)-case.