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.
Original language | English |
---|---|
Pages (from-to) | 229-245 |
Journal | Potential Analysis |
Volume | 37 |
Issue number | 3 |
Early online date | 26 Aug 2011 |
DOIs | |
Publication status | Published - Oct 2012 |
Keywords
- math.CO
- 31C20, 05C63, 05C81, 05C22
- discrete potential theory
- linear analysis on graphs
- discrete harmonic functions
- infinite graphs