On the collision between two PNG droplets
Probability
2011-08-15 v2
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.
Keywords
Cite
@article{arxiv.math/0603382,
title = {On the collision between two PNG droplets},
author = {Cristian Coletti and Leandro P. R. Pimentel},
journal= {arXiv preprint arXiv:math/0603382},
year = {2011}
}
Comments
Revised version with a new title and many corrections, 18 pages, 6 figures