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.
Keywords: 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},
year = {2011},
publisher = {EDP-Sciences},
volume = {15},
doi = {10.1051/ps/2009015},
mrnumber = {2870513},
zbl = {1263.60021},
language = {en},
url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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
Cité par Sources :