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

  • Raphaël Rossignol (a1) and Marie Théret (a2)

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 [9] obtained for boxes of particular orientation.

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Keywords

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

  • Raphaël Rossignol (a1) and Marie Théret (a2)

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