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

Raphaël Rossignol; Marie Théret

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 70-104
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Rossignol, Raphaël, and Théret, Marie. "Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation." ESAIM: Probability and Statistics 17 (2013): 70-104. <http://eudml.org/doc/273633>.

@article{Rossignol2013,
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.},
author = {Rossignol, Raphaël, Théret, Marie},
journal = {ESAIM: Probability and Statistics},
keywords = {first passage percolation; maximal flow; large deviation principle},
language = {eng},
pages = {70-104},
publisher = {EDP-Sciences},
title = {Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation},
url = {http://eudml.org/doc/273633},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 70
EP - 104
AB - 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.
LA - eng
KW - first passage percolation; maximal flow; large deviation principle
UR - http://eudml.org/doc/273633
ER -

References

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