Excited random walk in two dimensions has linear speed

Abstract

Excited random walk is a process that has a drift to the right whenever it encounters a new vertex. The paper shows that in two dimensions it drifts to the right linearly in time.

7 pages

References in corpus (2)

• Excited random walk in three dimensions has positive speed
• Multi-excited random walks on integers

Cited by in corpus (7)

• On a general many-dimensional excited random walk
• Excited against the tide: A random walk with competing drifts
• Excited random walk against a wall
• On strict monotonicity of the speed for excited random walks in one dimension
• Monotonicity for excited random walk in high dimensions
• Positively and negatively excited random walks on integers, with branching processes
• Recurrence and transience of excited random walks on ${\mathbb{Z}}^d$ and strips