Color-position symmetry in interacting particle systems

The asymmetric simple exclusion process (ASEP) is the evolution of a collection of particles on the integer lattice; particles interact according to simple rules and can be of various colors (equivalently, classes). In 2008 Amir-Angel-Valko established an interesting property of such processes: the color-position symmetry. We will discuss a generalization of this result and its new applications to the asymptotic behavior of this class of models.