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Equivalence of boundary measures on covering trees of finite graphs

Published online by Cambridge University Press:  19 September 2008

Russell Lyons
Department of Mathematics, Indiana University, Bloomington, IN 47405-5701, USA


Let T be the universal covering tree of a finite graph, G. By analogy with an open problem concerning negatively curved covering manifolds, Kaimanovich asked when two of the three natural measure classes on ∂T can coincide, the three measures being harmonic measure, the Patterson measure, and visibility measure. We provide an almost complete answer and discuss related issues. The answer is quite surprising in some cases.

Research Article
Copyright © Cambridge University Press 1994

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