# A balanced excited random walk

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00514926
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Submitted on : Friday, September 3, 2010 - 5:39:35 PM
Last modification on : Tuesday, July 6, 2021 - 3:40:00 AM
Long-term archiving on: : Saturday, December 4, 2010 - 2:54:27 AM

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### Identifiers

• HAL Id : hal-00514926, version 1
• ARXIV : 1009.0741

### Citation

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

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