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Law of large numbers for the simple exclusion process. (English) Zbl 1080.60089

The authors consider the simple exclusion process on \(Z\), an interacting particle system. They perform a graphical construction of the process and define couplings and different classes of particles (these are key tools for the proofs). By using the subadditive ergodic theorem they show the hydrodynamic limit for a particular initial measure which satisfies a stationary condition required by the ergodic theorem, and then the result is extended to initial product measures.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F15 Strong limit theorems
82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
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References:

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