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On Roughly Transitive Amenable Graphs and Harmonic Dirichlet Functions

Gábor Elek and Gábor Tardos
Proceedings of the American Mathematical Society
Vol. 128, No. 8 (Aug., 2000), pp. 2479-2485
Stable URL: http://www.jstor.org/stable/119840
Page Count: 7
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On Roughly Transitive Amenable Graphs and Harmonic Dirichlet Functions
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Abstract

We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.

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