Pathlines in exclusion processes.

Trajectory data from observations of a random-walk process are often used to characterize macroscopic transport coefficients and to make inferences about motility mechanisms. Continuum equations describing the average moments of the position of an agent in an exclusion process are derived and validated with simulation data. Unlike standard noninteracting random walks, the moment equations for the exclusion process explicitly represent the interaction of agents since they depend on the averaged macroscopic agent density. Key issues associated with the validity of the continuum equations and interpretation of experimental data are discussed.