Heavy tails in last-passage percolation
| dc.creator | Hambly, Ben | |
| dc.creator | Martin, James B. | |
| dc.date | 2006-04-08 | |
| dc.date.accessioned | 2026-07-07T07:10:40Z | |
| dc.date.available | 2026-07-07T07:10:40Z | |
| dc.description | We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index alpha<2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape of optimal paths; these are expressed in terms of a family (indexed by alpha) of "continuous last-passage percolation" models in the unit square. In the extreme case alpha=0 (corresponding to a distribution with slowly varying tail) the asymptotic distribution of the optimal path can be represented by a random self-similar measure on [0,1], whose multifractal spectrum we compute. By extending the continuous last-passage percolation model to R^2 we obtain a heavy-tailed analogue of the Airy process, representing the limit of appropriately scaled vectors of passage times to different points in the plane. We give corresponding results for a directed percolation problem based on alpha-stable Levy processes, and indicate extensions of the results to higher dimensions. | |
| dc.description | 43 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0604189 | |
| dc.identifier | http://arxiv.org/abs/math/0604189 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111492 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B41 | |
| dc.title | Heavy tails in last-passage percolation | |
| dc.type | text |