On the small maximal flows in first passage percolation

Details On the small maximal flows in first passage percolation On the small maximal flows in first passage percolation

2006-07-11

arxiv.org/abs/math/0607252v3

Ann. Fac. Sci. Toulouse, 17 (1) : 207-219, 2008

Mathematics

Probability

11 pages, 2 figure; added references, changes on part 4.1

Scientific paper

We consider the standard first passage percolation on $\mathbb{Z}^{d}$: with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten proved in 1987 a law of large numbers for the rescaled flow. Chayes and Chayes established that the large deviations far away below its typical value are of surface order, at least for the Bernoulli percolation and cylinders of certain height. Thanks to another approach we extend here their result to higher cylinders, and we transport this result to the model of first passage percolation.

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