DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 137-144


Discrete Random Walks, DRW'03

Cyril Banderier and Christian Krattenthaler (eds.)

DMTCS Conference Volume AC (2003), pp. 137-144

author: Anders Karlsson
title: Some remarks concerning harmonic functions on homogeneous graphs
keywords: Discrete random walks, Dirichlet problem, radial variation, hyperbolic compactifications
abstract: We obtain a new result concerning harmonic functions on infinite Cayley graphs
: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of
. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.
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reference: Anders Karlsson (2003), Some remarks concerning harmonic functions on homogeneous graphs, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 137-144
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