We prove that almost every path of a random walk on a finitely generated non-amenable group converges in the compactification of the group introduced by W.J. Floyd. In fact, we consider the more general setting of ergodic cocycles of some semigroup of 1-Lipschitz maps of a complete metric space with a boundary constructed following Gromov. We obtain in addition that when the Floyd boundary of a...

We estimate the decay of correlations for some Markov maps on a countable states space. A necessary and suucient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of nitely many cylinders. Estimates are giv...