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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.
@article{PS_2013__17__70_0,
author = {Rossignol, Rapha\"el and Th\'eret, Marie},
title = {Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation},
journal = {ESAIM: Probability and Statistics},
pages = {70--104},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2011109},
mrnumber = {3007160},
zbl = {1290.60106},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011109/}
}
TY - JOUR AU - Rossignol, Raphaël AU - Théret, Marie TI - Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation JO - ESAIM: Probability and Statistics PY - 2013 SP - 70 EP - 104 VL - 17 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2011109/ DO - 10.1051/ps/2011109 LA - en ID - PS_2013__17__70_0 ER -
%0 Journal Article %A Rossignol, Raphaël %A Théret, Marie %T Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation %J ESAIM: Probability and Statistics %D 2013 %P 70-104 %V 17 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2011109/ %R 10.1051/ps/2011109 %G en %F PS_2013__17__70_0
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
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