Last-Passage Percolation with General Weight Distribution

J.B. Martin

2006, v.12, №2, 273-299

ABSTRACT

We survey the directed last-passage percolation} model.For certain specific distributions of the weights, very precise scaling limits have been obtained, which we outline briefly. However, the main focus is on results for general weight distributions. These include: conditions under which laws of large numbers hold for the passage-times; shape theorems for associated growth models; properties concerning passage-times near to the boundary for models in two dimensions; scaling limits which apply in the case of sufficiently heavy-tailed weights. We also describe various aspects of the model of queues in tandem, which is one of the motivations for the two-dimensional directed last-passage percolation model with general weights. We also give simulations showing trees of optimal paths for the percolation models and displaying the evolution of the growth models.

Keywords: last-passage percolation,growth model,shape theorem,heavy-tailed distribution

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