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

Kamil Kaleta and Katarzyna Pietruska-Pałuba

Stochastic Processes and their Applications, 2018, vol. 128, issue 11, 3897-3939

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.

Keywords: Subordinate Brownian motion; Sierpiński gasket; Random Feynman–Kac semigroup; Schrödinger operator; Random potential; Integrated density of states; Eigenvalues; Reflected process (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:11:p:3897-3939

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DOI: 10.1016/j.spa.2018.01.003

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