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Excited Random Walks: Results, Methods, Open Problems
by Elena Kosygina   Martin P. W. Zerner

Vol. 8 No. 1 (2013) P.105~P.157

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.

KEYWORDS
excited random walk, cookie walk, recurrence, transience, zero-one laws,

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60K35, 60K37, 60J80

MILESTONES