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

2009/12/18 by Rossignol, Raphaël, Théret, Marie
#60K35 #82B43. #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0912.3601

Abstract

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 (1984) obtained for boxes of particular orientation.

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