Poisson boundary of groups acting on R-trees

Francois Gautero (1) , Frédéric Mathéus (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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 groups in terms of the boundary of the free sub- group. We rely upon the description of Poisson boundaries by means of a topological compacti cation as developed by Kaimanovich. All the groups studied here share the property of admitting a su fficiently complicated action on some R-tree.

Mots clés: semi-direct products; Poisson boundary; random walks; free groups; hyperbolic and relatively hyperbolic groups; semi-direct products.

Domaines: Probabilités [math.PR]; Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Francois Gautero, Frédéric Mathéus. Poisson boundary of groups acting on R-trees. Israel Journal of Mathematics, 2012, 191 (2), pp.585-646. ⟨hal-00769021⟩