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.
Mots clés : large deviations, random growth model, Skorokhod embedding theorem
@article{PS_2011__15__217_0, author = {Ibrahim, Jean-Paul}, title = {Large deviations for directed percolation on a thin rectangle}, journal = {ESAIM: Probability and Statistics}, pages = {217--232}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2009015}, mrnumber = {2870513}, zbl = {1263.60021}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2009015/} }
TY - JOUR AU - Ibrahim, Jean-Paul TI - Large deviations for directed percolation on a thin rectangle JO - ESAIM: Probability and Statistics PY - 2011 SP - 217 EP - 232 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2009015/ DO - 10.1051/ps/2009015 LA - en ID - PS_2011__15__217_0 ER -
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. http://www.numdam.org/articles/10.1051/ps/2009015/
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