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Large deviations for directed percolationon a thin rectangle

Published online by Cambridge University Press:  05 January 2012

Jean-Paul Ibrahim
Jean-Paul Ibrahim*
Affiliation:
Universitéde Toulouse, Université Paul Sabatier, Institut de Mathématiques de Toulouse, 31062 Toulouse, France CNRS, Institut de Mathématiques de Toulouse UMR 5219, 31062 Toulouse, France. jibrahim@math.univ-toulouse.fr

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.

Keywords

Large deviationsrandom growth modelSkorokhod embedding theorem

Information

Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 217 - 232
Copyright
© EDP Sciences, SMAI, 2011

References

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