On the collision between two PNG droplets

Details On the collision between two PNG droplets On the collision between two PNG droplets

2006-03-15

arxiv.org/abs/math/0603382v2

Journal of Statistical Physics, Vol. 126, No. 6, March 2007

Mathematics

Probability

Revised version with a new title and many corrections, 18 pages, 6 figures

Scientific paper

10.1007/s10955-006-9272-y

In this article we study the interface generated by the collision between two cristals growing layer by layer on a one-dimensional substrate through random decomposition of particles. We relate this interface with the notion of beta-path in an equivalent directed polymer model and, by using asymptotics results from Baik and Rains (2000) and some hydrodynamic tools introduced by Cator and Groeenenboon (2005), we derive a law of large numbers for such a path and obtain some bounds for its fluctuations.

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