The purpose of this book is to provide a comprehensive discussion of the available results
for discrete time branching processes with random control functions. The independence of …

We consider a class of self-interacting random walks in deterministic or random
environments, known as excited random walks or cookie walks, on the d-dimensional …

We consider excited random walks (ERWs) on Z with a bounded number of iid cookies per
site without the nonnegativity assumption on the drifts induced by the cookies. Kosygina and …

In this paper we study a substantial generalization of the model of excited random walk
introduced in Electron. Commun. Probab. 8 (2003) 86–92 by Benjamini and Wilson. We …

We describe scaling limits of recurrent excited random walks (ERWs) on Z in iid cookie
environments with a bounded number of cookies per site. We allow both positive and …

The excited random walk as defined by Benjamini and Wilson [2] has a bias in some fixed
direction, a feature which is highly useful in its analysis. See eg [10] and references within …

We consider excited random walk on a strip. We assume that the cookies are positive and
that the total expected drift per site is less than 1/L where L is the width of the strip. We prove …

We consider one-dimensional excited random walks (ERWs) with iid Markovian cookie
stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an …

Several phase transitions for excited random walks on the integers are known to be
characterized by a certain drift parameter δ∈\mathbbR. For recurrence/transience the …

In this paper we consider an excited random walk (ERW) on Z in identically piled periodic
environment. This is a discrete time process on Z defined by parameters …