Optimal tail estimates for directed last passage site percolation with geometric random variables

Details Optimal tail estimates for directed last passage site percolation with geometric random variables Optimal tail estimates for directed last passage site percolation with geometric random variables

2001-12-16

arxiv.org/abs/math/0112162v1

Mathematics

Probability

AMS-LaTex, 41 pages, 17 figures

Scientific paper

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.

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