# The Poisson formula for groups with hyperbolic properties

@article{Kaimanovich1998ThePF, title={The Poisson formula for groups with hyperbolic properties}, author={Vadim A. Kaimanovich}, journal={Annals of Mathematics}, year={1998}, volume={152}, pages={659-692} }

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…

## 9 Citations

POISSON BOUNDARY OF GROUPS ACTING ON R-TREES

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We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic…

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