The Poisson formula for groups with hyperbolic properties.
The Poisson Boundary of Polycyclic Groups
Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces.
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
A Poisson formula for harmonic projections
Random walks on the affine group of local fields and of homogeneous trees
The affine group of a local field acts on the tree (the Bruhat-Tits building of ) with a fixed point in the space of ends . More generally, we define the affine group of any homogeneous tree as the group of all automorphisms of with a common fixed point in , and establish main asymptotic properties of random products in : (1) law of large numbers and central limit theorem; (2) convergence to and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...
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