Directed Percolation and Generalized Friendly Walkers

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

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