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The Lifschitz singularity for the density of states on the Sierpinski gasket
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  • Published: March 1991

The Lifschitz singularity for the density of states on the Sierpinski gasket

  • Katarzyna Pietruska-Paluba1 nAff2 

Probability Theory and Related Fields volume 89, pages 1–33 (1991)Cite this article

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  • 16 Citations

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Summary

We prove the existence of the density of states for the Laplacian on the infinite Sierpinski gasket. Then the Lifschitz-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 ℝd-case.

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Author notes
  1. Katarzyna Pietruska-Paluba

    Present address: Warsaw University, Warsaw, Poland

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    Katarzyna Pietruska-Paluba

Authors
  1. Katarzyna Pietruska-Paluba
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Pietruska-Paluba, K. The Lifschitz singularity for the density of states on the Sierpinski gasket. Probab. Th. Rel. Fields 89, 1–33 (1991). https://doi.org/10.1007/BF01225823

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  • Received: 17 May 1990

  • Revised: 26 November 1990

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01225823

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Sierpinski Gasket
  • Brownian Trajectory
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