Volume 17, 2013
|Page(s)||70 - 104|
|Published online||18 December 2012|
Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation
1 Université Paris Sud, Laboratoire de
Mathématiques, bâtiment 425, 91405
2 École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm, 75230 Paris Cedex 05, France.
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  obtained for boxes of particular orientation.
Mathematics Subject Classification: 60K35 / 82B43
Key words: First passage percolation / maximal flow / large deviation principle.
© EDP Sciences, SMAI, 2012
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