On the shape of the connected components of the complement of two-dimensional Brownian random interlacements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912269002080256 |
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| author | Collin, Orphée Popov, Serguei |
| author_facet | Collin, Orphée Popov, Serguei |
| contents | We study the limiting shape of the connected components of the vacant set of two-dimensional Brownian random interlacements: we prove that the connected component around $x$ is close in distribution to a rescaled \emph{Brownian amoeba} in the regime when the distance from $x\in\mathbb{C}$ to the closest trajectory is small (which, in particular, includes the cases $x\to\infty$ with fixed intensity parameter $α$, and $α\to\infty$ with fixed $x$). We also obtain a new family of martingales built on the conditioned Brownian motion, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the shape of the connected components of the complement of two-dimensional Brownian random interlacements Collin, Orphée Popov, Serguei Probability 60K35, 60J65 We study the limiting shape of the connected components of the vacant set of two-dimensional Brownian random interlacements: we prove that the connected component around $x$ is close in distribution to a rescaled \emph{Brownian amoeba} in the regime when the distance from $x\in\mathbb{C}$ to the closest trajectory is small (which, in particular, includes the cases $x\to\infty$ with fixed intensity parameter $α$, and $α\to\infty$ with fixed $x$). We also obtain a new family of martingales built on the conditioned Brownian motion, which may be of independent interest. |
| title | On the shape of the connected components of the complement of two-dimensional Brownian random interlacements |
| topic | Probability 60K35, 60J65 |
| url | https://arxiv.org/abs/2410.08944 |