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15 April 2007 Harmonicity of Gibbs measures
Chris Connell, Roman Muchnik
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Duke Math. J. 137(3): 461-509 (15 April 2007). DOI: 10.1215/S0012-7094-07-13732-3

Abstract

We show that any continuous measure ν in the class of a generalized Gibbs stream on the boundary of a CAT(κ) group G arises as a harmonic measure for a random walk on G. Under an additional mild hypothesis on G and for ν, Hölder equivalent to a Gibbs measure, we show that (G,ν) arises as a Poisson boundary for a random walk on G. We also prove a new approximation theorem for general metric measure spaces giving quite flexible conditions for a set of functions to be a positive basis for the cone of positive continuous functions

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Chris Connell. Roman Muchnik. "Harmonicity of Gibbs measures." Duke Math. J. 137 (3) 461 - 509, 15 April 2007. https://doi.org/10.1215/S0012-7094-07-13732-3

Information

Published: 15 April 2007
First available in Project Euclid: 6 April 2007

zbMATH: 1133.60032
MathSciNet: MR2309151
Digital Object Identifier: 10.1215/S0012-7094-07-13732-3

Subjects:
Primary: 20F67 , 37A35 , 41A65 , 60J50

Rights: Copyright © 2007 Duke University Press

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Vol.137 • No. 3 • 15 April 2007
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