Abstract
We discuss the relationship between the isospectral profile and the spectral distribution of a Laplace operator on a countable group. In the case of locally finite countable groups, we emphasize the relevance of the metric associated to a natural Markov operator: it is an ultra-metric whose balls are optimal sets for the isospectral profile.
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Mathematics Subject Classification (2000). Primary: 60B15, 20F65; Secondary: 58C40.
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References
Alexander Bendikov, Barbara Bobikau, and Christophe Pittet, Spectral properties of a class of random walks on locally finite groups, preprint.
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© 2011 Springer Basel AG
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Bendikov, A., Bobikau, B., Pittet, C. (2011). Some Spectral and Geometric Aspects of Countable Groups. In: Lenz, D., Sobieczky, F., Woess, W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel. https://doi.org/10.1007/978-3-0346-0244-0_12
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DOI: https://doi.org/10.1007/978-3-0346-0244-0_12
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Online ISBN: 978-3-0346-0244-0
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