Infinite paths in randomly oriented lattices

The square lattice is used to generate an oriented graph in which a rightward or upward arrow is present on each edge with probability a , and a leftward or downward arrow with probability b . Independence between different edges of the square lattice is assumed, but nothing is assumed concerning the dependence between the two possible orientations at any given edge. A property of self‐duality is exploited to show that, when a + b =1, the process is, in a sense to be made precise, either critical or supercritical, but not subcritical. This observation enables progress with the percolation problem in which each horizontal edge is oriented rightward with probability p and otherwise leftward, and each vertical edge is oriented upward with probability p and otherwise downward. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18, 257–266, 2001