Limit behavior of linearly edge-reinforced random walks on the half-line
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915746792079360 |
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| author | Hu, Zechun Song, Renming Wang, Li |
| author_facet | Hu, Zechun Song, Renming Wang, Li |
| contents | Motivated by the article [M. Takei, Electron. J. Probab. 26 (2021), article no. 104], we study the limit behavior of linearly edge-reinforced random walks on the half-line $\mathbb{Z}_+$ with reinforcement parameter $δ>0$, and each edge $\{x,x+1\}$ has the initial weight $x^α\ln^βx$ for $x > 1$ and $1$ for $x = 0, 1$. The aim of this paper is to study the almost sure limit behavior of the walk in the recurrent regime, and extend the results of Takei mentioned above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit behavior of linearly edge-reinforced random walks on the half-line Hu, Zechun Song, Renming Wang, Li Probability Motivated by the article [M. Takei, Electron. J. Probab. 26 (2021), article no. 104], we study the limit behavior of linearly edge-reinforced random walks on the half-line $\mathbb{Z}_+$ with reinforcement parameter $δ>0$, and each edge $\{x,x+1\}$ has the initial weight $x^α\ln^βx$ for $x > 1$ and $1$ for $x = 0, 1$. The aim of this paper is to study the almost sure limit behavior of the walk in the recurrent regime, and extend the results of Takei mentioned above. |
| title | Limit behavior of linearly edge-reinforced random walks on the half-line |
| topic | Probability |
| url | https://arxiv.org/abs/2601.15627 |