A balanced excited random walk

Abstract

The following random process on ${\mathbb{Z}}^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove that this process is almost surely transient. The lower dimensional versions are discussed and various generalizations and related questions are proposed.

References in corpus (2)

• A survey of random processes with reinforcement
• Excited against the tide: A random walk with competing drifts