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

摘要

Equip the edges of the lattice $\mathbb{Z}^2$ with i.i.d. random capacities.A law of large numbers is known for the maximal flow crossing a rectangle in$\mathbb{R}^2$ when the side lengths of the rectangle go to infinity. We provethat the lower large deviations are of surface order, and we prove thecorresponding large deviation principle from below. This extends and improvesprevious large deviations results of Grimmett and Kesten (1984) obtained forboxes of particular orientation.