  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.
