Functional limit theorems for elephant random walks on general periodic structures
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914156682149888 |
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| author | Shibata, Shuhei |
| author_facet | Shibata, Shuhei |
| contents | This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional limit theorems for elephant random walks on general periodic structures Shibata, Shuhei Probability 60F17, 60K35, 05C81 This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk. |
| title | Functional limit theorems for elephant random walks on general periodic structures |
| topic | Probability 60F17, 60K35, 05C81 |
| url | https://arxiv.org/abs/2511.10347 |