Sharp asymptotics for $N$-point correlation functions of coalescing heavy-tailed random walk
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911407829680128 |
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| author | Yu, Jinjiong |
| author_facet | Yu, Jinjiong |
| contents | We study a system of coalescing continuous-time random walks starting from every site on $\mathbb{Z}$, where the jump increments lie in the domain of attraction of an $α$-stable distribution with $α\in(0,1]$. We establish sharp asymptotics for the $N$-point correlation function of the system. Our analysis relies on two precise tail estimates for the system density, as well as the non-collision probability of $N$ independent random walks with arbitrary fixed initial configurations. In addition, we derive refined estimates for heavy-tailed random walks, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp asymptotics for $N$-point correlation functions of coalescing heavy-tailed random walk Yu, Jinjiong Probability Primary: 82C22, Secondary: 60K35, 82C41 We study a system of coalescing continuous-time random walks starting from every site on $\mathbb{Z}$, where the jump increments lie in the domain of attraction of an $α$-stable distribution with $α\in(0,1]$. We establish sharp asymptotics for the $N$-point correlation function of the system. Our analysis relies on two precise tail estimates for the system density, as well as the non-collision probability of $N$ independent random walks with arbitrary fixed initial configurations. In addition, we derive refined estimates for heavy-tailed random walks, which may be of independent interest. |
| title | Sharp asymptotics for $N$-point correlation functions of coalescing heavy-tailed random walk |
| topic | Probability Primary: 82C22, Secondary: 60K35, 82C41 |
| url | https://arxiv.org/abs/2505.05000 |