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arXiv · 2511.16459

Elephants explore in spirals sometimes

Lucile Laulin·Bastien Mallein
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Abstract

We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the $n$th step is given by a random rotation of one of the previous steps chosen uniformly at random. We obtain a central limit theorem for this process, which shows that the process follows a randomly rotated logarithmic spiral at large times, with Gaussian fluctuations.

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Lucile Laulin, Bastien Mallein. 2025-11-20. Elephants explore in spirals sometimes. https://arxiv.org/abs/2511.16459

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