FLUCTUATION-DISSIPATION EQUATION OF ASYMMETRIC SIMPLE EXCLUSION PROCESSES

We consider asymmetric simple exclusion processes on the lattice Z(d) in dimension d greater than or equal to 3. We denote by L the generato r of the process, del the lattice gradient, eta the configuration, and w the current of the dynamics associated to the conserved quantity. W e prove that the fluctuation-dissipation equation w = Lu + D del eta h as a solution for some function u and some constant D identified to be the diffusion coefficient. Intuitively, Lu represents rapid fluctuati on and this equation describes a decomposition of the current into flu ctuation and gradient of the density held, representing the dissipatio n. Using this result, we proved rigorously that the Green-Kubo formula converges and it can be identified as the diffusion coefficient.