Duke Mathematical Journal
- Duke Math. J.
- Volume 137, Number 3 (2007), 461-509.
Harmonicity of Gibbs measures
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
Duke Math. J., Volume 137, Number 3 (2007), 461-509.
First available in Project Euclid: 6 April 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J50: Boundary theory 20F67: Hyperbolic groups and nonpositively curved groups 37A35: Entropy and other invariants, isomorphism, classification 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
Connell, Chris; Muchnik, Roman. Harmonicity of Gibbs measures. Duke Math. J. 137 (2007), no. 3, 461--509. doi:10.1215/S0012-7094-07-13732-3. https://projecteuclid.org/euclid.dmj/1175865518