Abstract
This Note deals with the dimension of the harmonic measure ν associated with a random walk on the isometry group of a Gromov hyperbolic space. We establish a link of the form dim ν ⩽ 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. To cite this article: V. Le Prince, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
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