Extension of results on generalized Pólya's urns for polynomially self-repelling walks
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915832948326400 |
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| author | Kosygina, Elena Marêché, Laure Mountford, Thomas Peterson, Jonathon |
| author_facet | Kosygina, Elena Marêché, Laure Mountford, Thomas Peterson, Jonathon |
| contents | This is a technical note which extends the results of Kosygina, Mountford and Peterson (Ann. Probab., 51(5):1684-1728, 2023, Section 4) about generalized Pólya's urns from a specific weight function $w(n) = (n+1)^{-α}$ to a general family of weight functions satisfying $(w(n))^{-1}=n^α\left(1+2Bn^{-1}+O\left(n^{-2}\right)\right)$ as $n \to \infty$. The latter was considered by Tóth (Ann. Probab., 24(3):1324-1367, 1996) as a part of his study of polynomially self-repelling walks. This extension will be used in forthcoming developments concerning scaling limits of these walks and related processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extension of results on generalized Pólya's urns for polynomially self-repelling walks Kosygina, Elena Marêché, Laure Mountford, Thomas Peterson, Jonathon Probability 60K35 (Primary) 60J10 (Secondary) This is a technical note which extends the results of Kosygina, Mountford and Peterson (Ann. Probab., 51(5):1684-1728, 2023, Section 4) about generalized Pólya's urns from a specific weight function $w(n) = (n+1)^{-α}$ to a general family of weight functions satisfying $(w(n))^{-1}=n^α\left(1+2Bn^{-1}+O\left(n^{-2}\right)\right)$ as $n \to \infty$. The latter was considered by Tóth (Ann. Probab., 24(3):1324-1367, 1996) as a part of his study of polynomially self-repelling walks. This extension will be used in forthcoming developments concerning scaling limits of these walks and related processes. |
| title | Extension of results on generalized Pólya's urns for polynomially self-repelling walks |
| topic | Probability 60K35 (Primary) 60J10 (Secondary) |
| url | https://arxiv.org/abs/2603.03622 |