Nonamenable Liouville Graphs
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.
KeywordsHarmonic Function Binary Tree Cayley Graph General Graph Harmonic Measure
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