The Poisson formula for groups with hyperbolic properties

  title={The Poisson formula for groups with hyperbolic properties},
  author={V. Kaimanovich},
  journal={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… Expand