Harmonicity of Gibbs measures

Chris Connell; Roman Muchnik

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Harmonicity of Gibbs measures

Chris Connell·Roman Muchnik

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Abstract

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 $α$-quasiconformal assumptions is that we must restrict our attention to CAT($-κ$) 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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Chris Connell, Roman Muchnik. 2005-07-02. Harmonicity of Gibbs measures. https://arxiv.org/abs/math/0507033

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