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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06759 |
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| _version_ | 1866916089446793216 |
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| author | Ransford, Julian |
| author_facet | Ransford, Julian |
| contents | We consider a simplified model of first-passage percolation, involving two families of i.i.d. random variables $\{ξ_{ij}\}$ and $\{η_{ij}\}$ corresponding to the weights of the horizontal and vertical edges respectively. We obtain an explicit formula for the limiting shape of the first-passage distance expressed in terms of the corresponding limit shapes of the two sets of weights for the Seppäläinen--Johansson model. We also study the limiting fluctuations of this model when at least one of the sets of weights is Bernoulli distributed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit shape formulas for a generalized Seppäläinen-Johansson model Ransford, Julian Probability We consider a simplified model of first-passage percolation, involving two families of i.i.d. random variables $\{ξ_{ij}\}$ and $\{η_{ij}\}$ corresponding to the weights of the horizontal and vertical edges respectively. We obtain an explicit formula for the limiting shape of the first-passage distance expressed in terms of the corresponding limit shapes of the two sets of weights for the Seppäläinen--Johansson model. We also study the limiting fluctuations of this model when at least one of the sets of weights is Bernoulli distributed. |
| title | Limit shape formulas for a generalized Seppäläinen-Johansson model |
| topic | Probability |
| url | https://arxiv.org/abs/2401.06759 |