Limiting distributions for a polynuclear growth model with external sources
Probability
2007-05-23 v1 Mathematical Physics
Combinatorics
math.MP
Abstract
The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources, which was considered by Pr\"ahofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory, or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.
Cite
@article{arxiv.math/0003130,
title = {Limiting distributions for a polynuclear growth model with external sources},
author = {Jinho Baik and Eric Rains},
journal= {arXiv preprint arXiv:math/0003130},
year = {2007}
}
Comments
15 pages, 1 figure, LaTex