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

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  • Kaleta, Kamil
  • Pietruska-Pałuba, Katarzyna

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.

Suggested Citation

  • Kaleta, Kamil & Pietruska-Pałuba, Katarzyna, 2018. "Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3897-3939.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3897-3939
    DOI: 10.1016/j.spa.2018.01.003
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    References listed on IDEAS

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    1. Kaleta, Kamil & Pietruska-Pałuba, Katarzyna, 2015. "Integrated density of states for Poisson–Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1244-1281.
    2. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
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