Invariant Measures for aTwo

We consider a process of two classes of particles jumping on a one dimensional lattice. The marginal system of the rst class of particles is the one dimensional totally asymmetric simple exclusion process. When classes are disregarded the process is also the totally asymmetric simple exclusion process. The existence of a unique invariant measure with product marginals with density and for the rst and rst plus second class particles, respectively, was shown by Ferrari, Kipnis and Saada (1991). Recently Der-rida, Janowsky, Lebowitz and Speer (1993) and Speer (1994) have computed this invariant measure for nite boxes and performed the innnite volume limit. Based on this computation we give a complete description of the measure and derive some of its properties. In particular we show that the invariant measure for the simple exclusion process as seen from a second class particle with asymptotic densities and is equivalent to the product measure with densities to the left of the origin and to the right of the origin.