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
References in corpus (7)
- Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
- Statistical Self-Similarity of One-Dimensional Growth Processes
- Second class particles and cube root asymptotics for Hammersley's process
- Competition interfaces and second class particles
- Hammersley's process with sources and sinks
- Roughening and inclination of competition interfaces
- Diffusive fluctuations for one-dimensional totally asymmetric interacting random dynamics