Law of large numbers for the maximal flow through tilted cylinders in two-dimensional first passage percolation

AbstractEquip the edges of the lattice Z2 with i.i.d. random capacities. We prove a law of large numbers for the maximal flow crossing a rectangle in R2 when the side lengths of the rectangle go to infinity. The value of the limit depends on the asymptotic behaviour of the ratio of the height of the cylinder over the length of its basis. This law of large numbers extends the law of large numbers obtained in Grimmett and Kesten (1984) [6] for rectangles of particular orientation