Geodesic
Large deviations for directed percolation on a thin rectangle
ESAIM: Probability and Statistics, Tome 15 (2011), pp. 217-232

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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.

DOI : 10.1051/ps/2009015
Classification : 60F10
Keywords: large deviations, random growth model, Skorokhod embedding theorem 
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Ibrahim, Jean-Paul. Large deviations for directed percolation on a thin rectangle. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 217-232. doi: 10.1051/ps/2009015

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