Beyond Gaussian Transport: Rare Events, Disorder, and Geometry

Transport in complex media is often understood through typical behavior: Gaussian spreading, ordinary response to forcing, and boundaries that merely confine motion. Yet some of the most revealing physics lies precisely where these expectations fail. In this talk I will discuss how rare fluctuations, strong disorder, and geometric constraints can qualitatively reshape transport, producing effects that are impossible to infer from average behavior alone. These include universal non-Gaussian statistics, counterintuitive mobility in confinement, and directed motion emerging from reflection itself. The broader message is that in disordered systems, rare events are not just corrections to the main story. They can be the mechanism.