Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dimensional properties of the harmonic measure for a random walk on a hyperbolic group


Author: Vincent Le Prince
Journal: Trans. Amer. Math. Soc. 359 (2007), 2881-2898
MSC (2000): Primary 60G50, 20F67, 28D20, 28A78
Published electronically: January 26, 2007
MathSciNet review: 2286061
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $ \nu$ associated with such a random walk. We first establish a link of the form $ \dim \nu\leq h/l$ between the dimension of the harmonic measure, the asymptotic entropy $ h$ of the random walk and its rate of escape $ l$. Then we use this inequality to show that the dimension of this measure can be made arbitrarily small and deduce a result on the type of the harmonic measure.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60G50, 20F67, 28D20, 28A78

Retrieve articles in all journals with MSC (2000): 60G50, 20F67, 28D20, 28A78


Additional Information

Vincent Le Prince
Affiliation: IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex, France
Email: vincent.leprince@univ-rennes1.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04108-6
PII: S 0002-9947(07)04108-6
Keywords: Ergodic theory, random walk, hyperbolic group, harmonic measure, entropy
Received by editor(s): December 16, 2004
Received by editor(s) in revised form: June 17, 2005
Published electronically: January 26, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.