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Boundaries and random walks on finitely generated infinite groups
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2003 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 41, no 2, 295-306 p.Article in journal (Refereed) Published
Abstract [en]

We prove that almost every path of a random walk oil a finitely generated nonamenable group converges in the compactification of the group introduced by W. J. Floyd. In fact, we consider the more general setting of ergodic cocycles of some semigroup of one-Lipschitz maps of a complete metric space with a boundary constructed following Gromov. We obtain in addition that when the Floyd boundary of a finitely generated group is non-trivial, then it is in fact maximal in the sense that it can be identified with the Poisson boundary of the group with reasonable measures. The proof relies on works of Kaimanovich together with visibility properties of Floyd boundaries. Furthermore, we discuss mean proximality of partial derivative Gamma and a conjecture of McMullen. Lastly, related statements about the convergence of certain sequences of points, for example quasigeodesic rays or orbits of one-Lipschitz maps, are obtained.

Place, publisher, year, edition, pages
2003. Vol. 41, no 2, 295-306 p.
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URN: urn:nbn:se:kth:diva-121750DOI: 10.1007/BF02390817ISI: 000232312300006OAI: diva2:619675

QC 20130506

Available from: 2013-05-06 Created: 2013-05-03 Last updated: 2013-05-06Bibliographically approved

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