Rough walks in random environment

Abstract: 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 stochastic differential equations, 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 permitting, we shall elaborate on the main tools to tackle these problems. Based on joint works with Olga Lopusanschi, with Jean-Dominique Deuschel and Nicolas Perkowski and with Johaness Bäumler, Noam Berger and Martin Slowik.

dynamical systemsprobability

Audience: researchers in the topic

( slides | video )

Horowitz seminar on probability, ergodic theory and dynamical systems