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Nonamenable Liouville Graphs

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

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.

Keywords

  • Harmonic Function
  • Binary Tree
  • Cayley Graph
  • General Graph
  • Harmonic Measure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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