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• W2950573411 abstract "We consider last-passage 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 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 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 problem based on alpha-stable Levy processes, and indicate extensions of the results to higher dimensions." @default.
• W2950573411 created "2019-06-27" @default.
• W2950573411 creator A5056672381 @default.
• W2950573411 creator A5065589370 @default.
• W2950573411 date "2006-04-08" @default.
• W2950573411 modified "2023-09-27" @default.
• W2950573411 title "Heavy tails in last-passage percolation" @default.
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• W2950573411 hasPublicationYear "2006" @default.
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