A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

Details A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy

2011-05-10

arxiv.org/abs/1105.2049v1

Mathematics

Combinatorics

Scientific paper

We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also extend a necessary existence criterion for non-elusive non-constant harmonic functions of finite energy due to Georgakopoulos.

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