### Abstract

We introduce the notion of rough transitivity and prove that there exist no non-constant harmonic Dirichlet functions on amenable roughly transitive graphs.

Original language | English |
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Pages (from-to) | 2479-2485 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 8 |

Publication status | Published - Dec 1 2000 |

### Keywords

- Amenable graphs
- Harmonic functions

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Elek, G., & Tardos, G. (2000). On roughly transitive amenable graphs and harmonic dirichlet functions.

*Proceedings of the American Mathematical Society*,*128*(8), 2479-2485.