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July 2005 Competition interfaces and second class particles
Pablo A. Ferrari, Leandro P. R. Pimentel
Ann. Probab. 33(4): 1235-1254 (July 2005). DOI: 10.1214/009117905000000080

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 ℤ2. 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.

Citation

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Pablo A. Ferrari. Leandro P. R. Pimentel. "Competition interfaces and second class particles." Ann. Probab. 33 (4) 1235 - 1254, July 2005. https://doi.org/10.1214/009117905000000080

Information

Published: July 2005
First available in Project Euclid: 1 July 2005

MathSciNet: MR2150188
zbMATH: 1078.60083
Digital Object Identifier: 10.1214/009117905000000080

Subjects:
Primary: 60K35
Secondary: 82B

Keywords: Asymmetric simple exclusion , Burgers equation , competition interface , Last-passage percolation , Rarefaction fan , Second class particle

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 4 • July 2005
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