Excited random walks: results, methods, open problems

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.

37 pages, 4 figures; minor revision

References in corpus (4)

• A survey of random processes with reinforcement
• Maximum occupation time of a transient excited random walk on Z
• Self-interacting random walks
• Snakes and perturbed random walks

Cited by in corpus (6)

• Excited random walk with periodic cookies
• Solution manifold and Its Statistical Applications
• Random walks with local memory
• Recurrence of horizontal-vertical walks
• A functional limit theorem for for excited random walks
• Speed of excited random walks with long backward steps