Branching capacity and Brownian snake capacity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914689065156608 |
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| author | Bai, Tianyi Delmas, Jean-François Hu, Yueyun |
| author_facet | Bai, Tianyi Delmas, Jean-François Hu, Yueyun |
| contents | The branching capacity has been introduced by [Zhu 2016] as the limit of the hitting probability of a symmetric branching random walk in $\mathbb Z^d$, $d\ge 5$. Similarly, we define the Brownian snake capacity in $\mathbb R^d$, as the scaling limit of the hitting probability by the Brownian snake starting from afar. Then, we prove our main result on the vague convergence of the rescaled branching capacity towards this Brownian snake capacity. Our proof relies on a precise convergence rate for the approximation of the branching capacity by hitting probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Branching capacity and Brownian snake capacity Bai, Tianyi Delmas, Jean-François Hu, Yueyun Probability 60F05, 60J45, 60J80 The branching capacity has been introduced by [Zhu 2016] as the limit of the hitting probability of a symmetric branching random walk in $\mathbb Z^d$, $d\ge 5$. Similarly, we define the Brownian snake capacity in $\mathbb R^d$, as the scaling limit of the hitting probability by the Brownian snake starting from afar. Then, we prove our main result on the vague convergence of the rescaled branching capacity towards this Brownian snake capacity. Our proof relies on a precise convergence rate for the approximation of the branching capacity by hitting probabilities. |
| title | Branching capacity and Brownian snake capacity |
| topic | Probability 60F05, 60J45, 60J80 |
| url | https://arxiv.org/abs/2402.13735 |