Optimal Tail Estimates for Directed Last Passage Site Percolation with Geometric Random Variables
J. Baik
Department of Mathematics, Princeton University
P. Deift
Courant Institute of Mathematical Sciences,
New York University
K. T.-R. McLaughlin
Department of Mathematics, University of North
Carolina, Chapel Hill
P. D. Miller
Department of Mathematics, University of Michigan,
Ann Arbor
X. Zhou
Department of Mathematics, Duke University
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.