Harmonic measures versus quasiconformal measures for hyperbolic groups
Sébastien Blachère; Peter Haïssinsky; Pierre Mathieu
Annales scientifiques de l'École Normale Supérieure (2011)
- Volume: 44, Issue: 4, page 683-721
- ISSN: 0012-9593
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topBlachère, Sébastien, Haïssinsky, Peter, and Mathieu, Pierre. "Harmonic measures versus quasiconformal measures for hyperbolic groups." Annales scientifiques de l'École Normale Supérieure 44.4 (2011): 683-721. <http://eudml.org/doc/272118>.
@article{Blachère2011,
abstract = {We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.},
author = {Blachère, Sébastien, Haïssinsky, Peter, Mathieu, Pierre},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {hyperbolic groups; random walks on groups; harmonic measures; quasiconformal measures; dimension of a measure; Martin boundary; brownian motion; Green metric},
language = {eng},
number = {4},
pages = {683-721},
publisher = {Société mathématique de France},
title = {Harmonic measures versus quasiconformal measures for hyperbolic groups},
url = {http://eudml.org/doc/272118},
volume = {44},
year = {2011},
}
TY - JOUR
AU - Blachère, Sébastien
AU - Haïssinsky, Peter
AU - Mathieu, Pierre
TI - Harmonic measures versus quasiconformal measures for hyperbolic groups
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2011
PB - Société mathématique de France
VL - 44
IS - 4
SP - 683
EP - 721
AB - We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
LA - eng
KW - hyperbolic groups; random walks on groups; harmonic measures; quasiconformal measures; dimension of a measure; Martin boundary; brownian motion; Green metric
UR - http://eudml.org/doc/272118
ER -
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