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This 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 ≤ 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 harmonicdoi:10.1090/s0002-9947-07-04108-6 fatcat:x5q3uxqm6be3zcm5al726dchy4