Strongly vertex-reinforced jump process on graphs with bounded degree
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917817831391232 |
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| author | Collevecchio, Andrea Nguyen, Tuan-Minh |
| author_facet | Collevecchio, Andrea Nguyen, Tuan-Minh |
| contents | We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement function $w$ is reciprocally integrable and non-decreasing, then the process visits only a finite number of vertices. In the case where $w$ is approximately equal to a super-linear polynomial, we show that the process eventually gets stuck on a star-shaped subgraph and there is exactly one vertex with unbounded local time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strongly vertex-reinforced jump process on graphs with bounded degree Collevecchio, Andrea Nguyen, Tuan-Minh Probability 60G17, 60K35, 60G20 We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement function $w$ is reciprocally integrable and non-decreasing, then the process visits only a finite number of vertices. In the case where $w$ is approximately equal to a super-linear polynomial, we show that the process eventually gets stuck on a star-shaped subgraph and there is exactly one vertex with unbounded local time. |
| title | Strongly vertex-reinforced jump process on graphs with bounded degree |
| topic | Probability 60G17, 60K35, 60G20 |
| url | https://arxiv.org/abs/2401.04366 |