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arXiv:0911.0616 [math.PR]AbstractReferencesReviewsResources

Poisson boundary of groups acting on real trees

François Gautero, Frédéric Mathéus

Published 2009-11-03, updated 2011-01-07Version 3

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. We rely upon the description of Poisson boundaries by means of a topological compactification as developed by Kaimanovich. All the groups studied here share the property of admitting a sufficiently complicated action on some real tree.

Comments: 42 pages. This is a majorly revised version. The introduction is completely rewritten, the statements are simplified. A new section entitled "The method" is added just after the introduction. More details are given on the case of a direct product of two finitely generated free groups
Categories: math.PR, math.GT
Subjects: 20F65, 60J50, 20F67, 60B15, 20P05
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