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Book Sections Year : 2011

Some spectral and geometric aspects of countable groups

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.

Dates and versions

hal-01305041 , version 1 (20-04-2016)

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Alexander Bendikov, Barbara Bobikau, Christophe Pittet. Some spectral and geometric aspects of countable groups. Random Walks, Boundaries and Spectra, 64, Springer Basel AG, pp.227-234, 2011, Progress in Probability, 978-3-0346-0243-3. ⟨10.1007/978-3-0346-0244-0_12⟩. ⟨hal-01305041⟩
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