Presentations

Joint work with Makiko Sasada. Hydrodynamic limit is a rigorous method to derive macroscopic partial differential equations as limits from microscopic stochastic large-scale interacting systems. The macroscopic diffusion equations that appear as limits are described via the “diffusion matrices”, and determining these matrices is the first crucial step in proving the hydrodynamic limit. In this talk, we will construct discrete harmonic theory for configuration spaces of microscopic large-scale interacting systems, and we define the Hodge period matrices for these configuration spaces. These period matrices are expected to coincide with the diffusion matrices of the hydrodynamic limits. If this expectation is valid, our result provides an interpretation of the diffusion matrices as period matrices of the configuration spaces.