Lamplighter graphs do not admit harmonic functions of finite energy

Georgakopoulos, Agelos

doi:10.1090/S0002-9939-2010-10279-4

Lamplighter graphs do not admit harmonic functions of finite energy
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by Agelos Georgakopoulos PDF

Proc. Amer. Math. Soc. 138 (2010), 3057-3061

Abstract:

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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