Large deviations for directed percolation on a thin rectangle

Details Large deviations for directed percolation on a thin rectangle Large deviations for directed percolation on a thin rectangle

2007-12-20

arxiv.org/abs/0712.3421v2

Mathematics

Probability

20 pages

Scientific paper

Following the recent investigations of Baik and Suidan in \cite{baik2005gcl} and Bodineau and Martin in \cite{bodineau2005upl}, we prove large deviation properties for a last-passage percolation model in $\mathbb{Z}^{2}_{+}$ 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 \cite{baik2005gcl} and \cite{bodineau2005upl}, on an embedding in Brownian paths and the KMT approximation. The study of the subexponential case completes the exposition.

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