Volume 15, 2011
|Page(s)||217 - 232|
|Published online||05 January 2012|
Large deviations for directed percolation on a thin rectangle
1 Universitéde Toulouse, Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, France
2 CNRS, Institut de Mathématiques de Toulouse UMR 5219, 31062 Toulouse, France
Received: 18 December 2007
Revised: 13 February 2009
Following the recent investigations of Baik and Suidan in [Int. Math. Res. Not. (2005) 325–337] and Bodineau and Martin in [Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ+2 whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, Int. Math. Res. Not. (2005) 325–337] and [T. Bodineau and J. Martin, Electron. Commun. Probab. 10 (2005) 105–112 (electronic)], on an embedding in Brownian paths and the KMT approximation. The study of the subexponential case completes the exposition.
Mathematics Subject Classification: 60F10
Key words: Large deviations / random growth model / Skorokhod embedding theorem
© EDP Sciences, SMAI, 2011
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