On large deviation regimes for random media models

Details On large deviation regimes for random media models On large deviation regimes for random media models

2009-06-23

arxiv.org/abs/0906.4254v1

Annals of Applied Probability 2009, Vol. 19, No. 2, 826-862

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP535 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP535

The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time $a_n$ on $\mathbb{Z}^d$ and a last passage percolation time $Z_n$. For these functionals, we have $\lim_{n\to\infty}\frac{a_n}{n}=\nu$ and $\lim_{n\to\infty}\frac{Z_n}{n}=\mu$. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.

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