Ryoichiro Noda

Scaling limit of the collision measure for two-dimensional random walks

We study the scaling limit of the collision measure of two i.i.d. discrete-time random walks on $\mathbb Z^2$, which records their collision sites and times. This is a critical regime for collisions: the walks collide infinitely often, whereas the limiting Brownian motions do not collide at positive times. Hence, exist...