A balanced excited random walk

Itai Benjamini (1) , Gady Kozma (1) , Bruno Schapira (2)

1 Department of Computer Science and Applied Mathematics [Rehovot]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

The following random process on $\Z^4$ 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.

Mots clés: Excited random walk; Self-interacting process; Excited random walk.

Domaines: Probabilités [math.PR]

Itai Benjamini, Gady Kozma, Bruno Schapira. A balanced excited random walk. 2010. ⟨hal-00514926⟩