Probability and Statistics Seminar——Sample-path Large Deviation Principle and Microcanonical Variational Principle for a 2-d Stochastic Interacting Vortex Dynamics
报告人：Chenyang Chen (Peking University)
地点：Room 1114, Sciences Building No. 1
Abstract: We are interested in characterizing large time coherent structures of a 2-D stochastic interacting vortex dynamics, which takes Navier-Stokes equation as the mean field limit. First, we obtain two sample path large deviation principles with the same rate function for this model when the number of vortices goes to infinity, one is in the finite-energy space and the other is in the probability space under the assumption of finite initial energy. Second, we prove that the large time limit of large deviation rate function is exactly the entropy functional, independent of the Reynolds number. Moreover, we derive an equilibrium microcanonical variational principle in Onsager-Joyce-Montgomery theory from such a non-equilibrium stochastic model, the solution of which characterizes the large time coherent structure.