Properties of the limit shape for some last-passage growth models in random environments

Hao Lin and Timo Seppäläinen

Stochastic Processes and their Applications, 2012, vol. 122, issue 2, 498-521

Abstract: We study directed last-passage percolation on the planar square lattice whose weights have general distributions, or equivalently, queues in series with general service distributions. Each row of the last-passage model has its own randomly chosen weight distribution. We investigate the limiting time constant close to the boundary of the quadrant. Close to the y-axis, where the number of random distributions averaged over stays large, the limiting time constant takes the same universal form as in the homogeneous model. But close to the x-axis we see the effect of the tail of the distribution of the random environment.

Keywords: Corner growth model; Random environment; Limit shape; Last-passage percolation; Queues in series (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2011.08.015

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