Differentiability of limit shapes in continuous first passage percolation models
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929385766912000 |
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| author | Bakhtin, Yuri Dow, Douglas |
| author_facet | Bakhtin, Yuri Dow, Douglas |
| contents | We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which that limit shape can be shown to be differentiable. We then describe examples of continuous first passage percolation models that fit into this framework. The first example is of a family of Riemannian first passage percolation models and the second is a discrete time model based on Poissonian points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differentiability of limit shapes in continuous first passage percolation models Bakhtin, Yuri Dow, Douglas Probability 60K37, 82B44, 60K35 We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which that limit shape can be shown to be differentiable. We then describe examples of continuous first passage percolation models that fit into this framework. The first example is of a family of Riemannian first passage percolation models and the second is a discrete time model based on Poissonian points. |
| title | Differentiability of limit shapes in continuous first passage percolation models |
| topic | Probability 60K37, 82B44, 60K35 |
| url | https://arxiv.org/abs/2406.09652 |