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

Published online by Cambridge University Press:  06 December 2012

Raphaël Rossignol  and
Marie Théret
Raphaël Rossignol
Affiliation:
Université Paris Sud, Laboratoire de Mathématiques, bâtiment 425, 91405 Orsay Cedex, France.. raphael.rossignol@math.u-psud.fr
Marie Théret
Affiliation:
École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm, 75230 Paris Cedex 05, France. ; marie.theret@ens.fr
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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.

Keywords

First passage percolationmaximal flowlarge deviation principle.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 70 - 104
Copyright
© EDP Sciences, SMAI, 2012

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