  In this paper we show that a variety of interacting particle systems with
multiple species can be viewed as random walks on Hecke algebras. This class of
systems includes the asymmetric simple exclusion process (ASEP), M-exclusion
TASEP, ASEP(q,j), stochastic vertex models, and many others. As an application,
we study the asymptotic behavior of second class particles in some of these
systems.
