We use Brownian dynamics simulation of bead-rod chains to model the electrophoresis of double-stranded DNA molecules through dilute post arrays, in which post spacings are large relative to the Kuhn step. We first consider hairpin collisions with a single post in strong electric fields and generalize these results to describe electrophoresis through post arrays in which chains completely relax between collisions. We develop expressions relating chain velocity (or mobility) and dispersion to chain length and post density and then evaluate these predictions from the single-post model by simulating chain migration through dilute arrays of randomly positioned posts. We find that the single-post model is limited to very dilute arrays in which only weak separations are generated. During electrophoresis through random arrays, the formation of hairpins is found to be most frequent at moderate electric field strengths where both hairpin formation and chain relaxation are important. By determining streamwise dispersion coefficients, we evaluate the performance of dilute random arrays as separation devices and make comparisons with other techniques. Finally, after simulating chain migration through ordered arrays (i.e., square and hexagonal arrangements), we find that disordered post arrangements are essential for separations in strong electric fields. (C) 2003 American Institute of Physics.