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
jibrahim@math.univ-toulouse.fr

Received: 18 December 2007
Revised: 13 February 2009

Abstract

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.