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