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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On roughly transitive amenable graphs and harmonic Dirichlet functions


Authors: Gábor Elek and Gábor Tardos
Journal: Proc. Amer. Math. Soc. 128 (2000), 2479-2485
MSC (1991): Primary 58G05
Published electronically: February 25, 2000
MathSciNet review: 1657731
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Abstract:

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


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Additional Information

Gábor Elek
Affiliation: Rényi Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: elek@math-inst.hu

Gábor Tardos
Affiliation: Rényi Institute of the Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary
Email: tardos@math-inst.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05288-6
PII: S 0002-9939(00)05288-6
Keywords: Amenable graphs, harmonic functions
Received by editor(s): July 6, 1998
Received by editor(s) in revised form: September 8, 1998
Published electronically: February 25, 2000
Additional Notes: The first author was supported by OTKA grant T25004 and the Bolyai Fellowship.
The second author was supported by OTKA grants F014919, T029255 and AKP grant 97-56.
Communicated by: Józef Dodziuk
Article copyright: © Copyright 2000 American Mathematical Society