Competition interfaces and second class particles

@article{Ferrari2004CompetitionIA,
  title={Competition interfaces and second class particles},
  author={Pablo A. Ferrari and Leandro P. R. Pimentel},
  journal={Annals of Probability},
  year={2004},
  volume={33},
  pages={1235-1254}
}
The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z 2 . We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an… 

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