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.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
Full Text: DOI


[1] De Masi, J. Stat. Phys. 55 pp 787– (1989)
[2] , , and , A survey of the hydrodynamical behavior of many particle systems, pp. 123–294 in: Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, and , eds., North-Holland, Amsterdam-New York, 1984.
[3] and , Bulk diffusion for interacting Brownian particles, pp. 41–49 in: Statistical Physics and Dynamical Systems, , and , eds., Birkhäuser, Boston, 1985.
[4] Kipnis, Comm. Math. Phys. 104 pp 1– (1986)
[5] Quastel, Comm. Pure Appl. Math. 45 pp 623– (1992)
[6] , and , in preparation.
[7] Rezakhanlou, Comm. Math. Phys.
[8] Large Scale Dynamics for Interacting Particles, Part B: Stochastic Lattice Gases. Springer-Verlag, Berlin-New York, 1991.
[9] and , Multidimensional Diffusion Processes, Springer-Verlag, New York. 1979. · Zbl 0426.60069
[10] Sznitman, Lecture Notes in Math. 1464 pp 165– (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.