Once-Reinforced and Self-Interacting Random Walks beyond exchangeability
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915479258398720 |
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| author | Collevecchio, Andrea Tarrès, Pierre |
| author_facet | Collevecchio, Andrea Tarrès, Pierre |
| contents | We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove large deviations estimates for the range of the walk to have cardinality of the order $N^{d/(d+2)}$ in dimension larger than or equal than two. We also prove that ORRW is transient on all non-amenable graphs for small reinforcement.~Moreover, we study the shape of oriented ORRW on euclidean lattices.
We also provide a new approach to the study of general self-interacting random walk, which we apply to random walk in random environment, reinforced processes on oriented graphs, including the directed ORRW. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Once-Reinforced and Self-Interacting Random Walks beyond exchangeability Collevecchio, Andrea Tarrès, Pierre Probability 60K35, 60K37 We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove large deviations estimates for the range of the walk to have cardinality of the order $N^{d/(d+2)}$ in dimension larger than or equal than two. We also prove that ORRW is transient on all non-amenable graphs for small reinforcement.~Moreover, we study the shape of oriented ORRW on euclidean lattices. We also provide a new approach to the study of general self-interacting random walk, which we apply to random walk in random environment, reinforced processes on oriented graphs, including the directed ORRW. |
| title | Once-Reinforced and Self-Interacting Random Walks beyond exchangeability |
| topic | Probability 60K35, 60K37 |
| url | https://arxiv.org/abs/2509.04318 |