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Nonamenable Liouville Graphs

  • Itai Benjamini
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, 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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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Itai Benjamini
    • 1
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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