Large deviations for directed percolation on a thin rectangle

Jean-Paul Ibrahim

ESAIM: Probability and Statistics (2012)

  • Volume: 15, page 217-232
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Ibrahim, Jean-Paul. "Large deviations for directed percolation on a thin rectangle." ESAIM: Probability and Statistics 15 (2012): 217-232. <http://eudml.org/doc/222485>.

@article{Ibrahim2012,
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.},
author = {Ibrahim, Jean-Paul},
journal = {ESAIM: Probability and Statistics},
keywords = {Large deviations; random growth model; Skorokhod embedding theorem; large deviations},
language = {eng},
month = {1},
pages = {217-232},
publisher = {EDP Sciences},
title = {Large deviations for directed percolation on a thin rectangle},
url = {http://eudml.org/doc/222485},
volume = {15},
year = {2012},
}

TY - JOUR
AU - Ibrahim, Jean-Paul
TI - Large deviations for directed percolation on a thin rectangle
JO - ESAIM: Probability and Statistics
DA - 2012/1//
PB - EDP Sciences
VL - 15
SP - 217
EP - 232
AB - 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.
LA - eng
KW - Large deviations; random growth model; Skorokhod embedding theorem; large deviations
UR - http://eudml.org/doc/222485
ER -

References

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