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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.15049 |
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| _version_ | 1866916956386361344 |
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| author | Fang, Zheng |
| author_facet | Fang, Zheng |
| contents | We study how conditioning affects the long-term behavior of the Elephant Random Walk, focusing on its first return to the origin, namely, the time it takes to forget the training. When the walker is conditioned to be at position $n$ at time $n$, this return time scales as $n^{(4-4p)/(3-4p)}$ in the diffusive regime, and grows exponentially in the critical regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How long does it take an Elephant Random Walk to forget its training Fang, Zheng Probability 60J10 60F17 60G42 We study how conditioning affects the long-term behavior of the Elephant Random Walk, focusing on its first return to the origin, namely, the time it takes to forget the training. When the walker is conditioned to be at position $n$ at time $n$, this return time scales as $n^{(4-4p)/(3-4p)}$ in the diffusive regime, and grows exponentially in the critical regime. |
| title | How long does it take an Elephant Random Walk to forget its training |
| topic | Probability 60J10 60F17 60G42 |
| url | https://arxiv.org/abs/2509.15049 |