Tim Hulshof (TU Eindhoven)

A scaling limit for random walk in a very restrictive random environment
Random walk on a lattice has Brownian motion as its scaling limit. Random walk on a slightly damaged lattice also has a Brownian scaling limit. But when the damage is so severe that the lattice (almost) falls apart into only finite pieces, the random walk suddenly moves orders of magnitude more slowly, and the scaling limit (if it exists) must have dramatically different properties. This extreme slow-down has played a central role in the study of random walk in random environments in the past four decades. It is, however, not clear whether this extreme slow-down is a natural phenomenon, or is due to pathologies in the construction of the process. The talk is about progress on this question.
(joint work with Remco van der Hofstad and Jan Nagel)