Jonathon Peterson

Convergence of excited random walks on Markovian cookie stacks to Brownian motion perturbed at extrema

Excited random walks are a class of self-interacting random walks where the transition probabilities depend on the local time of the walk at the present site. It has previously been shown, only for certain special cases, that when the walk is recurrent the limiting distribution of the rescaled path of the walk is a Brownian motion perturbed at its extrema. We extend this convergence to a much more general class of excited random walks: excited random walks on Markovian cookie stacks. For this we develop a completely new approach to proving convergence to perturbed Brownian motion. Previously, it was already know that generalized Ray-Knight Theorems for the excited random walk were consistent with convergence to perturbed Brownian motion. We use improved versions of these generalized Ray-Knight Theorems to construct a coupling of the random walk with a perturbed Brownian motion. This talk is based on joint work with Elena Kosygina and Tom Mountford.