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

  • Lin, Hao
  • Seppäläinen, Timo
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002237
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 2 ()
    Pages: 498-521

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:498-521
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    1. Andjel, E. D. & Ferrari, P. A. & Guiol, H. & Landim *, C., 2000. "Convergence to the maximal invariant measure for a zero-range process with random rates," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 67-81, November.
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