Unified study of the phase transition for block-weighted random planar maps
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914832897277952 |
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| author | Salvy, Zéphyr |
| author_facet | Salvy, Zéphyr |
| contents | In [Fleurat, Salvy 2024], we introduced a model of block-weighted random maps that undergoes a phase transition as the density of separating elements changes. The purpose of this note is to demonstrate that the methodology we developed can be extended to many other families of maps. We prove that a phase transition exists and provide detailed information about the size of the largest blocks in each regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unified study of the phase transition for block-weighted random planar maps Salvy, Zéphyr Probability Combinatorics 05C12, 05C80, 60D05, 60F17, 68R05, 82B41 In [Fleurat, Salvy 2024], we introduced a model of block-weighted random maps that undergoes a phase transition as the density of separating elements changes. The purpose of this note is to demonstrate that the methodology we developed can be extended to many other families of maps. We prove that a phase transition exists and provide detailed information about the size of the largest blocks in each regime. |
| title | Unified study of the phase transition for block-weighted random planar maps |
| topic | Probability Combinatorics 05C12, 05C80, 60D05, 60F17, 68R05, 82B41 |
| url | https://arxiv.org/abs/2406.08139 |