Asymptotic Solution of Interacting Walks in One Dimension

An asymptotic solution to interacting walks in one dimension is presented. For repulsive and attractive interactions, respectively, the model describes aspects of uncorrelated diffusion on a lattice with sources or with randomly distributed traps. In the latter case, the average number of sites visited varies with the number of steps in the walk as $N^{\frac{1}{3}}$, while the survival probability decays as $N^{-\frac{1}{3}}\exp (-b{N}^{\frac{1}{3}})$, improving on previous predictions for diffusion with traps.