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Competition interfaces and second class particles

Pablo A. Ferrari·Leandro P. R. Pimentel
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Abstract

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 asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface.

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Pablo A. Ferrari, Leandro P. R. Pimentel. 2005-08-25. Competition interfaces and second class particles. https://doi.org/10.1214/009117905000000080

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