The distinction between regular and disordered random walks breaks down in two or more spatial dimensions if the regular random walks have broken global spatial symmetries. A better classification for regular random walks is ‘‘integrable’’ and ‘‘nonintegrable.’’ It may be impossible to distinguish the dynamics of a nonintegrable regular random walk from the dynamics of a disordered random walk.

• Received 30 May 1995

DOI:https://doi.org/10.1103/PhysRevE.52.4516