%0 Journal Article
%T Harmonicity of Gibbs measures
%A Chris Connell
%A Roman Muchnik
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0507033v1