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

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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.
AMS-LaTex, 41 pages, 17 figures

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Probability, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/62899

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0112162
 http://arxiv.org/abs/math/0112162

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arXiv