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Fluctuations from the hydrodynamical limit for the symmetric simple exclusion in \(\mathbb{Z}{}^ d\). (English) Zbl 0754.60127

The fluctuation field of the symmetric simple exclusion on \(\mathbb{Z}^ d\) is shown to converge to a generalized Ornstein-Uhlenbeck process in the hydrodynamic limit. The results are obtained using the martingale characterization of Holley and Stroock and estimates of the two point correlation functions.

MSC:

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