Phase transition on the fluctuation of the structure of random walk ranges
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908890652737536 |
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| author | Adhikari, Arka Okada, Izumi |
| author_facet | Adhikari, Arka Okada, Izumi |
| contents | We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in the scaling behavior of these fluctuations, leading to qualitatively different regimes, with a distinct phase transition in dimension 6. In particular, we remark that convergence in dimension 6 occurs with a non-standard rescaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07304 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase transition on the fluctuation of the structure of random walk ranges Adhikari, Arka Okada, Izumi Probability We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in the scaling behavior of these fluctuations, leading to qualitatively different regimes, with a distinct phase transition in dimension 6. In particular, we remark that convergence in dimension 6 occurs with a non-standard rescaling. |
| title | Phase transition on the fluctuation of the structure of random walk ranges |
| topic | Probability |
| url | https://arxiv.org/abs/2602.07304 |