Abstract
We show that any continuous measure in the class of a generalized Gibbs stream on the boundary of a CAT() group arises as a harmonic measure for a random walk on . Under an additional mild hypothesis on and for , Hölder equivalent to a Gibbs measure, we show that arises as a Poisson boundary for a random walk on . 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
Citation
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
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