Lamplighter graphs do not admit harmonic functions of finite energy

Details Lamplighter graphs do not admit harmonic functions of finite energy Lamplighter graphs do not admit harmonic functions of finite energy

2009-07-08

arxiv.org/abs/0907.1398v2

Mathematics

Group Theory

Scientific paper

We prove that a lamplighter graph of a locally finite graph over a finite
graph does not admit a non-constant harmonic function of finite Dirichlet
energy.

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