Harmonic measures versus quasiconformal measures for hyperbolic groups
  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. 
S\'ebastien Blach\`ere (LATP), Peter Ha\"issinsky (LATP), Pierre   Mathieu (LATP)