Quantitative homogenization and hydrodynamic limit of non-gradient exclusion process

Abstract

For the non-gradient exclusion process, we prove the quantitative homogenization of the diffusion matrix and the conductivity by local functions. The proof relies on the renormalization approach developed by Armstrong, Kuusi, Mourrat, and Smart, while the new challenge here is the hard core constraint of particle number on every site. Therefore, a coarse-grained method is proposed to lift the configuration to a larger space without exclusion, and a gradient coupling between two systems is applied to capture the spatial cancellation. We then strengthen the convergence rate to be uniform concerning the density, and integrate it into the work by Funaki, Uchiyama, and Yau [IMA Vol. Math. Appl., 77 (1996), pp. 1-40.] to yield a quantitative hydrodynamic limit. Our new approach avoids showing the characterization of closed forms and provides stronger results. The extension is discussed for the model in the presence of disorder on the bonds.