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

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  • Lin, Hao
  • Seppäläinen, Timo

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.

Suggested Citation

  • Lin, Hao & Seppäläinen, Timo, 2012. "Properties of the limit shape for some last-passage growth models in random environments," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 498-521.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:498-521
    DOI: 10.1016/j.spa.2011.08.015
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    References listed on IDEAS

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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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