The Annals of Probability

Competition interfaces and second class particles

Pablo A. Ferrari and Leandro P. R. Pimentel

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 33, Number 4 (2005), 1235-1254.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1120224580

Digital Object Identifier
doi:10.1214/009117905000000080

Mathematical Reviews number (MathSciNet)
MR2150188

Zentralblatt MATH identifier
1078.60083

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B

Keywords
Asymmetric simple exclusion second class particle Burgers equation rarefaction fan last-passage percolation competition interface

Citation

Ferrari, Pablo A.; Pimentel, Leandro P. R. Competition interfaces and second class particles. Ann. Probab. 33 (2005), no. 4, 1235--1254. doi:10.1214/009117905000000080. https://projecteuclid.org/euclid.aop/1120224580


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