An average self-avoiding random walk on the square lattice lasts 71 steps

Abstract

Attention is drawn to the fact that a self‐avoiding walker is remarkably localized because of self‐trapping. For the square lattice, where a walker may get trapped after any number n≥7 steps, we determine the distribution t(n) of walk lengths by a Monte Carlo calculation using 60 000 walks. The average walk length is found to be 70.7±0.2 steps. The average displacement of trapped walkers is merely 11.9 lattice units.