On the Collision between Two Png Droplets

@inproceedings{Pimentel2006OnTC,
  title={On the Collision between Two Png Droplets},
  author={Leandro P. R. Pimentel},
  year={2006}
}
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 β-path in an equivalent directed polymer model and, by using asymptotics results from Baik and Rains [3] and some hydrodynamic tools introduced by Cator and Groeenenboon [5], we derive a law of large numbers for such a path and obtain some bounds for its fluctuations.