Tal Orenshtein

Rough walks in random environment

Random walks in random environment have been extensively studied in the last half-century and invariance principles are known to hold in various cases. We shall discuss recent contributions, where the scaling limit is obtained in the rough path space for the lifted random walk. Except for the immediate application to SDEs, this provides new information on the structure of the limiting path - an enhanced Brownian motion with a linearly perturbed second level, which is characterized in various ways. Time permitted, we shall elaborate on the main tools to tackle these problems. The talk is based on joint works with Olga Lopusanschi, with Jean-Dominique Deuschel and Nicolas Perkowski and with Johaness Bäumler, Noam Berger and Martin Slowik.