Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 70-104.

Equip the edges of the lattice ℤ2 with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in ℝ2 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 [9] obtained for boxes of particular orientation.

DOI : 10.1051/ps/2011109
Classification : 60K35, 82B43
Mots clés : first passage percolation, maximal flow, large deviation principle 
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Rossignol, Raphaël; Théret, Marie. Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 70-104. doi : 10.1051/ps/2011109. http://www.numdam.org/articles/10.1051/ps/2011109/

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