05/01/2022, 16:00 — 17:00 — Online
Makiko Sasada, University of Tokyo
On Varadhan’s decomposition theorem in a general setting
We rigorously formulate and prove for a relatively general class of interactions the characterization of shift-invariant closed $L^2$-forms for a large scale interacting system. Such characterization of closed forms has played an essential role in proving the hydrodynamic limit of nongradient systems. The universal expression in terms of conserved quantities was sought from observations for specific models, but a precise formulation or rigorous proof up until now had been elusive. To obtain this, we first prove the universal characterization of shift-invariant closed “local” forms in a completely geometric way, that is, in a way that has nothing to do with probability measures. Then, we apply the result to characterize the $L^2$-forms. Our result is applicable for many important models including generalized exclusion processes, multi-species exclusion processes, exclusion processes on crystal lattices and so on. This talk is based on a joint work with Kenichi Bannai and Yukio Kametani, and a joint work with Kenichi Bannai.
