Directed Percolation and Generalized Friendly Walkers

TL;DR

This paper establishes a novel equivalence between directed percolation on arbitrary lattices and models of interacting directed random walkers, revealing connections to surface step interactions and self-avoiding walks, thus providing new insights into percolation phenomena.

Contribution

It introduces a new theoretical framework linking directed percolation to interacting random walkers and surface models, expanding understanding of percolation processes.

Findings

Directed percolation is equivalent to interacting directed random walkers.

In 1+1 dimensions, it relates to models of surface steps.

Connections to self-avoiding walks in isotropic percolation.

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.