Limit shape formulas for a generalized Sepp\'al\'ainen-Johansson model
| Autor: | Ransford, Julian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider a simplified model of first-passage percolation, involving two families of i.i.d. random variables $\{\xi_{ij}\}$ and $\{\eta_{ij}\}$ 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 Sepp\"al\"ainen--Johansson model. We also study the limiting fluctuations of this model when at least one of the sets of weights is Bernoulli distributed. Comment: 12 pages, 2 figures |
| Databáze: | arXiv |
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