Harmonicity of Gibbs measures

Details Harmonicity of Gibbs measures Harmonicity of Gibbs measures

2005-07-02

arxiv.org/abs/math/0507033v1

Mathematics

Group Theory

Scientific paper

In this paper we extend the construction of random walks with a prescribed Poisson boundary to the case of measures in the class of a generalized Gibbs state. The price for dropping the $\alpha$-quasiconformal assumptions is that we must restrict our attention to CAT($-\kappa$) groups. Apart from the new estimates required, we prove a new approximation scheme to provide a positive basis for positive functions in a metric measure space.

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