Elephants explore in spirals sometimes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915628677332992 |
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| 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 |