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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the eigenspaces of lamplighter random walks and percolation clusters on graphs


Author: Franz Lehner
Journal: Proc. Amer. Math. Soc. 137 (2009), 2631-2637
MSC (2000): Primary 43A05, 47B80, 60K35
Published electronically: March 17, 2009
MathSciNet review: 2497475
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09869-4
PII: S 0002-9939(09)09869-4
Keywords: Wreath product, percolation, random walk, spectral measure, point spectrum, eigenfunctions
Received by editor(s): July 9, 2008
Published electronically: March 17, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.