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.References
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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