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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the eigenspaces of lamplighter random walks and percolation clusters on graphs
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by Franz Lehner PDF
Proc. Amer. Math. Soc. 137 (2009), 2631-2637 Request permission

Abstract:

We show that the Plancherel measure of the lamplighter random walk on a graph coincides with the expected spectral measure of the absorbing random walk on the Bernoulli percolation clusters. In the subcritical regime the spectrum is pure point and we construct a complete orthonormal basis consisting of finitely supported eigenfunctions.
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Additional Information
  • Franz Lehner
  • Affiliation: Institut für Mathematische Strukturtheorie, Steyrergasse 30, A-8010 Graz, Austria
  • Email: lehner@finanz.math.tu-graz.ac.at
  • Received by editor(s): July 9, 2008
  • Published electronically: March 17, 2009
  • Communicated by: Marius Junge
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2631-2637
  • MSC (2000): Primary 43A05, 47B80, 60K35
  • DOI: https://doi.org/10.1090/S0002-9939-09-09869-4
  • MathSciNet review: 2497475