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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.13074 |
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| _version_ | 1866916619466309632 |
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| author | Angel, Omer Jacob, Emmanuel Kolesnik, Brett Miermont, Grégory |
| author_facet | Angel, Omer Jacob, Emmanuel Kolesnik, Brett Miermont, Grégory |
| contents | The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The snake in the Brownian sphere Angel, Omer Jacob, Emmanuel Kolesnik, Brett Miermont, Grégory Probability 60D05 The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere. |
| title | The snake in the Brownian sphere |
| topic | Probability 60D05 |
| url | https://arxiv.org/abs/2502.13074 |