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

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

2010-09-25

arxiv.org/abs/1009.4967v3

Mathematics

Probability

24 pages, this paper has been accepted for publication in Stochastic Processes and their Applications

Scientific paper

10.1016/j.spa.2011.08.015

We study directed last passage percolation on the first quadrant of the planar square lattice whose weights have general distributions, or equivalently, ./G/1 queues in series. The service time distributions of the servers vary randomly which constitutes a random environment for the model. Equivalently, 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 means attached to the rows.

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