Directed Percolation and Generalized Friendly Walkers
arXiv:cond-mat/9902141 · doi:10.1103/PhysRevLett.82.2232
Abstract
We show that the problem of directed percolation on an arbitrary lattice is equivalent to the problem of m directed random walkers with rather general attractive interactions, when suitably continued to m=0. In 1+1 dimensions, this is dual to a model of interacting steps on a vicinal surface. A similar correspondence with interacting self-avoiding walks is constructed for isotropic percolation.
4 pages, 3 figures, to be published in Phys. Rev. Lett