# The Poisson formula for groups with hyperbolic properties

@article{Kaimanovich1998ThePF,
title={The Poisson formula for groups with hyperbolic properties},
journal={Annals of Mathematics},
year={1998},
volume={152},
pages={659-692}
}
• V. Kaimanovich
• Published 15 February 1998
• Mathematics
• Annals of Mathematics
The Poisson boundary of a group G with a probability measure „ is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an integral representation of bounded „-harmonic functions on G. In this paper we develop a new method of identifying the Poisson boundary based on entropy estimates for conditional random walks. It leads to simple purely geometric criteria of boundary maximality which…
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