94-71 Ferrari P.A., Fontes L.R.G., Kohayakawa Y.

Invariant Measures for a Two Species Asymmetric Process (68K, TeX) Mar 29, 94

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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.

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