Victor Gerasimov (Université de Belo Horizonte) : A characterization of hyperbolic groups in terms of random walks.

We are looking for properties of random walks on a group that hold for every hyperbolic group and fail for every non-hyperbolic group.
We are mainly interested in various versions of Ancona's property: if the Gromov product with respect to the word metric is zero then the Gromov product with respect to the Green metric
does not exceed some constant.