Central Limit Theorems for Gromov Hyperbolic Groups
2010 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 23, no 3, 871-887 p.Article in journal (Refereed) Published
In this paper we study asymptotic properties of symmetric and nondegenerate random walks on transient hyperbolic groups. We prove a central limit theorem and a law of iterated logarithm for the drift of a random walk, extending previous results by S. Sawyer and T. Steger and of F. Ledrappier for certain CAT(-1)-groups. The proofs use a result by A. Ancona on the identification of the Martin boundary of a hyperbolic group with its Gromov boundary. We also give a new interpretation, in terms of Hilbert metrics, of the Green metric, first introduced by S. Brofferio and S. BlachSre.
Place, publisher, year, edition, pages
2010. Vol. 23, no 3, 871-887 p.
Random walks on groups, Central limit theorems, Martingale approximations, Metric geometry, Ergodic theory
IdentifiersURN: urn:nbn:se:kth:diva-13950DOI: 10.1007/s10959-009-0230-xISI: 000280128700010ScopusID: 2-s2.0-77954761264OAI: oai:DiVA.org:kth-13950DiVA: diva2:328552
QC 20100705 Uppdaterad från submitted till published (20110215).2010-07-052010-07-052011-02-15Bibliographically approved