Excited random walks: results, methods, open problems
Probability
2013-05-15 v2
Abstract
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 integer lattice. The main purpose of this paper is two-fold: to give a survey of known results and some of the methods and to present several new results. The latter include functional limit theorems for transient one-dimensional excited random walks in bounded i.i.d. cookie environments as well as some zero-one laws. Several open problems are stated.
Cite
@article{arxiv.1204.1895,
title = {Excited random walks: results, methods, open problems},
author = {Elena Kosygina and Martin P. W. Zerner},
journal= {arXiv preprint arXiv:1204.1895},
year = {2013}
}
Comments
37 pages, 4 figures; minor revision