Fluctuations and their Glauber dynamics in lattice systems (Q1304656)

The authors consider a class of unbounded spin systems on the lattice \(Z^d\) and construct the stochastic dynamics in the fluctuation space [cf. \textit{S. Albeverio}, \textit{Y. Kondratiev} and \textit{M. Röckner}, ibid. 144, No. 2, 394-423 (1997; Zbl 0880.60098)]. It is shown that the generator \(H_\mu\) of the dynamics is constructed by the Dirichlet form of the macroscopic Gaussian measure, but including additionally a coefficient operator related to the original Dirichlet generator for the microscopic stochastic dynamics. Via transporting the generator \(H_\mu\) to the macroscopic fluctuation space, it is also shown that the corresponding generator is nothing but the one for the generalized Ornstein-Uhlenbeck process.