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Nonamenable Liouville Graphs

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arxiv 1010.3365 v1 pith:FGDJJGCA submitted 2010-10-16 math.MG math.PR

classification math.MGmath.PR
keywords graphleveladmitsbinaryboundededgesexpanderfunctions
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Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.

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