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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Kaleta, Kamil^1,2  Pietruska-Paluba, Katarzyna¹ 

[1] Univ Warsaw, Inst Math, Ul Banacha 2, PL-02097 Warsaw, Poland

[2] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

关键词: Subordinate Brownian motion;    Sierpinski gasket;    Random Feynman-Kac semigroup;    Schrodinger operator;    Random potential;    Integrated density of states;    Eigenvalues;    Reflected process;   

DOI  :  10.1016/j.spa.2018.01.003

来源: Elsevier

【 摘 要 】

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 Sierpinski gasket. We also study the long-time behaviour for the corresponding averaged Feynman-Kac functionals. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free