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Nonamenable Liouville Graphs

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Coarse Geometry and Randomness

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2100))

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Abstract

In this section we present an example of a bounded degree graph with a positive Cheeger constant (i.e. nonamenable graph) which is Liouville, that is, it admits no non constant bounded harmonic functions. This example shows that the theorem proved in Sect. 12 cannot be extended to general graphs.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Itai Benjamini

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  1. Itai Benjamini
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Benjamini, I. (2013). Nonamenable Liouville Graphs. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_13

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