In the particular model of a zero range jump process in equilibrium, the asymptotic covariances of the--spatially and temporally rescaled--particle number field are computed. The main tool in that computation is a general theorem, whose validity is established for the given class of processes, which states that the asymptotic behaviour of the covariances of any field corresponding to a local function is determined by a suitable projection of that field on the linear (here one-dimensional) space spanned by the fields of conserved quantities (here: the particle number).
"Equilibrium Fluctuations of Stochastic Particle Systems: The Role of Conserved Quantities." Ann. Probab. 12 (3) 742 - 759, August, 1984. https://doi.org/10.1214/aop/1176993225