Directed percolation: Shape of the percolation cone, conductivity exponents, and high-dimensionality behaviour

Presents several results for the directed percolation problem. The shape of the percolation cone is discussed, showing how the operating angle behaves near threshold, and explaining the orientation dependence of the correlation exponents found by Domany and Kinzel (1981). The Cayley tree model is used to discuss the high-dimensionality limit. The conductivity problem on a directed network is introduced, and the high-dimensionality values for the conductivity exponents s and tau are found.