A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy
classification
🧮 math.CO
keywords
finiteenergyfunctionsharmonicnon-constantadmittingcharacterizationcriterion
read the original abstract
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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.