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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


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.


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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.


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

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

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


Vol.33 • No. 4 • July 2005
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