Figure 2.

“Myopic self-avoiding random walk” on a two-dimensional grid. Panel (a) shows two successful transition events. The walkers, which started from the origin (0, 0), reached the right absorbing wall at x=15 before being absorbed by the left absorbing wall at x=−1. The upper trajectory crossed itself once at (4, 10), and the lower one avoided itself successfully during the whole transition. Panel (b) compares the distributions of the transition-event durations, obtained from brute force and WE simulation.