Discrete polynuclear growth and determinantal processes
Probability
2009-11-07 v2 Mathematical Physics
math.MP
Abstract
We consider a discrete polynuclear growth (PNG) process and prove a functioal limit theorem for its convergrence to the Airy process. This generalizes previous results by Pr"ahofer and Spohn. The result enables us to express the GOE largest eigenvalue (Tracy-Widom) distribution in terms of the Airy process. We also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem.
Cite
@article{arxiv.math/0206208,
title = {Discrete polynuclear growth and determinantal processes},
author = {Kurt Johansson},
journal= {arXiv preprint arXiv:math/0206208},
year = {2009}
}
Comments
In the new version some parts have been replaced, new material has beeb added and errors corrected