2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73243This paper deals with random walks on isometry groups of Gromov hyperbolic spaces, and more precisely with the dimension of the harmonic measure $ν$ associated with such a random walk. We first establish a link of the form $\dim ν\leq h/l$ 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.Dynamical SystemsMSC : 60J15, 20F67, 28D20, 28A78text