Central Limit Theorems for Gromov Hyperbolic Groups

Michael Björklund ()
Additional contact information
Michael Björklund: Royal Institute of Technology

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 871-887

Abstract: Abstract 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. Blachère.

Keywords: Random walks on groups; Central limit theorems; Martingale approximations; Metric geometry; Ergodic theory; 20F67; 60G50 (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-009-0230-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-009-0230-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-009-0230-x

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().