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Geodesic forests in last-passage percolation

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  • López, Sergio I.
  • Pimentel, Leandro P.R.

Abstract

The aim of this article is to study the forest composed by point-to-line geodesics in the last-passage percolation model with exponential weights. We will show that the location of the root can be described in terms of the maxima of a random walk, whose distribution will depend on the geometry of the substrate (line). For flat substrates, we will get power law behaviour of the height function, study its scaling limit, and describe it in terms of variational problems involving the Airy process.

Suggested Citation

  • López, Sergio I. & Pimentel, Leandro P.R., 2017. "Geodesic forests in last-passage percolation," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 304-324.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:1:p:304-324
    DOI: 10.1016/j.spa.2016.06.009
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    References listed on IDEAS

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    1. Cator, Eric & Pimentel, Leandro P.R., 2015. "On the local fluctuations of last-passage percolation models," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 538-551.
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