Excited random walk in three dimensions has positive speed

Abstract

Excited random walk is a random walk that has a positive drift to the right when it reaches a vertex it hasn't been to before. We show that in three dimensions the walk drifts to the right in non-zero speed.

13 pages

References in corpus (1)

• Loop-erased random walk on a torus in dimensions 4 and above

Cited by in corpus (7)

• Limit laws of transient excited random walks on integers
• Excited random walk in two dimensions has linear speed
• On the speed of the one-dimensional excited random walk in the transient regime
• Excited random walk against a wall
• Multi-excited random walks on integers
• Monotonicity for excited random walk in high dimensions
• Positively and negatively excited random walks on integers, with branching processes