Degenerate Competing Three-Particle Systems

Abstract

We study systems of three interacting particles, in which drifts and variances are assigned by rank. These systems are "degenerate": the variances corresponding to one or two ranks can vanish, so the corresponding ranked motions become ballistic rather than diffusive. Depending on which ranks are allowed to "go ballistic" the systems exhibit markedly different behavior which we study in some detail. Also studied are stability properties for the resulting planar process of gaps between successive ranks.