Upper large deviations for the maximal flow in first-passage percolation

We consider the standard first-passage percolation in for d>=2 and we denote by [phi]nd-1,h(n) the maximal flow through the cylinder ]0,n]d-1x]0,h(n)] from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension 3: under some assumptions, [phi]nd-1,h(n)/nd-1 converges towards a constant [nu]. We look now at the probability that [phi]nd-1,h(n)/nd-1 is greater than [nu]+[epsilon] for some [epsilon]>0, and we show under some assumptions that this probability decays exponentially fast with the volume nd-1h(n) of the cylinder. Moreover, we prove a large deviation principle for the sequence .