A phase transition for competition interfaces

Details A phase transition for competition interfaces A phase transition for competition interfaces

2007-01-15

arxiv.org/abs/math/0701418v2

Annals of Applied Probability 2009, Vol. 19, No. 1, 281-317

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP542 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP542

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle $\theta$ of the cone: for $\theta\geq180^{\circ}$, the direction is deterministic, while for $\theta<180^{\circ}$, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.

Affiliated with

Also associated with

No associations

Rating

A phase transition for competition interfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A phase transition for competition interfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A phase transition for competition interfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585391