Title: Generalized Ray-Knight theorems for excited random walks on Z and applications.

Abstract: Generalized Ray-Knight theorems for local times proved to be a very useful tool for the study of the limiting behavior of different types of self-interacting random walks on Z. Examples include several classes of reinforced random walks, excited random walks, and rotor walks with defects. We shall discuss our most recent results* about functional limit theorems for recurrent excited random walks on Markovian cookie stacks, give a more general picture, and discuss some open questions.
* Joint work with T. Mountford, EPFL, Switzerland, and J. Peterson, Purdue University.