Ballistic random walks in random environment as rough paths

We shall discuss an annealed functional CLT for ballistic RWRE in $(1/2)^-$-Hoelder rough path topology. An interesting phenomenon appears: the scaling limit of the area process is not only the Stratonovich Levy area but there is an addition of a linear term called the area anomaly. Moreover, the latter is identified in terms of the walk on a regeneration interval and naturally provides an extra information on the limiting process in case the correction is non-zero. Our result holds more generally, namely for any discrete process with bounded jumps which has a regular enough regenerative structure. This is a joint work with Olga Lopusanschi.