Shannon's theorem for locally compact groups (Q2119207)

The definition of the Poisson boundary is one of the result of this paper: the Poisson boundary can be defined as the space of ergodic components of the shift map on the path space, and it provides a generalization of the classical Poisson representation formula for bounded harmonic functions on the disk. The key result is the proof of a version of the Shannon-McMillan-Breiman theorem for locally compact groups. Several applications are given in this paper such as isometries of nonpositively curved spaces, as well as Diestel-Leader graphs and horocylic products.