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Propagation of chaos for symmetric simple exclusions. (English) Zbl 0808.60083

The symmetric simple exclusion process (SSEP) is a continuous time Markov process in which particles perform symmetric random walks on a lattice but are excluded to occupy the same site. It is one of the simplest lattice gas models that exhibits some of the behavior expected for a large class of interacting particle systems. The object of this article is to establish propagation of chaos type behavior for SSEP. Roughly speaking, we show that if particles are initially located independently on a lattice, then, despite interaction among them, the independence is restored asymptotically at later times. We assume that initially particles are distributed identically and we show that the evolution of a single marked particle is governed by an inhomogeneous Markov process that can be uniquely determined in terms of the initial distribution and certain transport coefficients.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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