Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation

Details Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation

2009-12-18

arxiv.org/abs/0912.3601v1

Mathematics

Probability

36 pages, 4 figures

Scientific paper

Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in $\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We prove that the lower large deviations are of surface order, and we prove the corresponding large deviation principle from below. This extends and improves previous large deviations results of Grimmett and Kesten (1984) obtained for boxes of particular orientation.

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