On the collision between two PNG droplets
arXiv:math/0603382 · doi:10.1007/s10955-006-9272-y
Abstract
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.
Revised version with a new title and many corrections, 18 pages, 6 figures