%0 Journal Article
%T Harmonic measures versus quasiconformal measures for hyperbolic groups
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%+ European Institute for Statistics, Probability, Stochastic Operations Research and its Applications (EURANDOM)
%+ Picard
%A Blachère, Sébastien
%A Haïssinsky, Peter
%A Mathieu, Pierre
%Z Besides minor modifications, we provide a new proof that the harmonic measure of a finitely supported random walk on a Fuchsian group with cusps is singular. 52 pp.
%< avec comité de lecture
%@ 0012-9593
%J Annales Scientifiques de l'École Normale Supérieure
%I Société mathématique de France
%V 44
%N no. 4
%P 683 -- 721
%8 2011
%D 2011
%Z 0806.3915
%K Hyperbolic groups
%K random walks on groups
%K harmonic measures
%K quasiconformal measures
%K dimension of a measure
%K Martin boundary
%K Brownian motion
%K Green metric
%Z 20F67, 60B15 (11K55, 20F69, 28A75, 60J50, 60J65)
%Z Mathematics [math]/Probability [math.PR]
%Z Mathematics [math]/Metric Geometry [math.MG]
%Z Mathematics [math]/Group Theory [math.GR]Journal articles
%X 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 \qc measures on the boundary of the group.
%G English
%2 https://hal.science/hal-00290127v2/document
%2 https://hal.science/hal-00290127v2/file/qcharm2.pdf
%L hal-00290127
%U https://hal.science/hal-00290127
%~ LATP
%~ CNRS
%~ UNIV-AMU
%~ INSMI
%~ I2M