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Optimal tail estimates for directed last passage site percolation with geometric random variables. (English) Zbl 1016.15022
Summary: 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 K. Johansson [Commun. Math. Phys. 209, No. 2, 437-476 (2000; Zbl 0969.15008)]. 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.

MSC:
15B52 Random matrices (algebraic aspects)
82B43 Percolation
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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