HAUSDORFF DIMENSION OF THE HARMONIC MEASURE ON TREES

Authors
KAIMANOVICH VA
Citation
Va. Kaimanovich, HAUSDORFF DIMENSION OF THE HARMONIC MEASURE ON TREES, Ergodic theory & dynamical systems, 18, 1998, pp. 631-660
Citations number
40
Categorie Soggetti
Mathematics,Mathematics
Journal title
Ergodic theory & dynamical systems → ACNP
ISSN journal
01433857
Volume
18
Year of publication
1998
Part
3
Pages
631 - 660
Database
ISI
SICI code
0143-3857(1998)18:<631:HDOTHM>2.0.ZU;2-S
Abstract
For a large class of Markov operators on trees we prove the formula HD nu = h/l connecting the Hausdorff dimension of the harmonic measure n u on the tree boundary, the rate of escape l and the asymptotic entrop y h. Applications of this formula include random walks on free groups, conditional random walks, random walks in random environment and rand om walks on treed equivalence relations.