Quantitative homogenization and hydrodynamic limit of non-gradient exclusion process

For the non-gradient exclusion process, we prove its approximation rate of diffusion matrix/conductivity by local functions. The proof follows the quantitative homogenization theory 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. Moreover, the approximation rate of conductivity is uniform with respect to the density via the regularity of the local corrector. As an application, we integrate this result in the work by Funaki, Uchiyama and Yau [IMA Vol. Math. Appl., 77 (1996), pp. 1-40.] and yield a quantitative hydrodynamic limit. In particular, our new approach avoids to show the characterization of closed forms. We also discuss the possible extensions in the presence of disorder on the bonds.