5,102 research outputs found
Competition interfaces and second class particles
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.Comment: Published at http://dx.doi.org/10.1214/009117905000000080 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …