We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry group of a Gromov hyperbolic space. This completes a result obtained by the author in a previous paper, where only an upper bound for the dimension was proved.
"A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space." Electron. Commun. Probab. 13 45 - 53, 2008. https://doi.org/10.1214/ECP.v13-1350