Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	张琦博士,北京雁栖湖应用数学研究院/清华大学丘成桐数学中心
Inviter:
Title:	Macroscopic coarse-grained dynamics: from most probable path to macroscopic fluctuation
Language:	Chinese
Time & Venue:	2023.07.12 16:00-17:00 南楼N913
Abstract:	Coarse-graining is the process of describing a high-dimensional and complex microscopic dynamics by an macroscopic dynamics. In this talk, we consider the overdamped Langevin dynamics as a microscopic dynamics model. The density and current, as macroscopic observables, are derived from the ensemble-averaged empirical density and current using conditional expectations and the law of large numbers. By employing the the Onsager-Machlup action functional, we determine the most probable path as the macroscopic dynamics. Additionally, we establish a large deviations principle for the ensemble-averaged empirical density and current. Finally, we compare these results with the hydrodynamical limit of stochastic lattice gases, as first considered by Guo, Papanicolaou, and Varadhan.