Optimal tail estimates for directed last passage site percolation with geometric random variables
Probability
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
In this paper, we obtain optimal uniform lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12]. The estimates are used to prove a lower tail moderate deviation result for the model. The estimates also imply the convergence of moments, and also provide a verification of the universal scaling law relating the longitudinal and the transversal fluctuations of the model.
Cite
@article{arxiv.math/0112162,
title = {Optimal tail estimates for directed last passage site percolation with geometric random variables},
author = {Jinho Baik and Percy Deift and Ken McLaughlin and Peter Miller and Xin Zhou},
journal= {arXiv preprint arXiv:math/0112162},
year = {2007}
}
Comments
AMS-LaTex, 41 pages, 17 figures