Elephants explore in spirals sometimes

Fuente: arXiv
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Main Authors: Laulin, Lucile, Mallein, Bastien
Format: Preprint
Published: 2025
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_version_ 1866915628677332992
author Laulin, Lucile
Mallein, Bastien
author_facet Laulin, Lucile
Mallein, Bastien
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16459
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Elephants explore in spirals sometimes
Laulin, Lucile
Mallein, Bastien
Probability
60G50, 60G42, 60J85
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.
title Elephants explore in spirals sometimes
topic Probability
60G50, 60G42, 60J85
url https://arxiv.org/abs/2511.16459