Diffusive motion in the presence of an array of interacting centers

The motion of a diffusing particle in an array of interacting centers is studied in one dimension, in terms of the positions of the centers and the intensities of the interactions. A sum of delta function potentials from the centers create the total potential which in one dimension can yield exact analytic solutions in special limits. The long time limit in the regions of weak interactions and strong repulsions are explicitly given and analyzed.