Ferrari P.A., Fontes L.R.G., Kohayakawa Y.
Invariant Measures for a Two Species Asymmetric Process
(68K, TeX)

ABSTRACT.  We consider a process of two classes of
particles jumping on a one dimensional lattice. The marginal system of
the first 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~$\rho$
and~$\lambda$ for the first and first plus second class particles,
respectively, was shown by Ferrari, Kipnis and Saada~(1991). Recently
Derrida, Janowsky, Lebowitz and Speer~(1993) and Speer (1994) have
computed this invariant measure for finite boxes and performed the
infinite 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~$\rho$ and~$\la$ is equivalent to the product measure with
densities~$\rho$ to the left of the origin and~$\la$ to the right of
the origin.