Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpi\'nski gasket

TL;DR

This paper investigates the spectral properties and long-time behavior of subordinate Brownian motions influenced by Poissonian potentials on the Sierpiński gasket, revealing Lifschitz-type singularities and their implications.

Contribution

It establishes Lifschitz-type singularities for the integrated density of states and analyzes the long-time behavior of Feynman-Kac functionals on fractal structures.

Findings

Lifschitz-type singularity near the spectrum's bottom

Asymptotic behavior of the integrated density of states

Long-time decay rates of Feynman-Kac functionals

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 Sierpi\'nski gasket. We also study the long-time behaviour for the corresponding averaged Feynman-Kac functionals.