Title: The Brownian web distance.
Abstract: Coalescing simple random walks in the plane form an infinite tree. A natural directed distance on this tree is given by the number of jumps between branches when one is only allowed to move in one direction. The Brownian web distance is the scale-invariant limit of this directed metric. It is integer-valued and has scaling exponents 0:1:2 as compared to 1:2:3 in KPZ universality. Yet, this model is still in the KPZ universality class. I will explain why. Joint work with Balint Veto.