Quantitative propagation of chaos for 2D stochastic vortex model on the whole space under moderate interactions

We derive the stochastic 2D vortex model on the whole Euclidean space from moderately interacting particle systems driven by individual and environmental noises, obtaining quantitative estimates in the sense of the entropy and energy functionals. The main novelties lie in combining the control of the Fisher information of the particle system with the Ladyzhenskaya and Donsker-Varadhan inequalities, as well as localization techniques within the probabilistic data setting, to address the nonlinearity and quadratic variation arising from Ito's formula. Moreover, we construct a suitable solution for the limiting process.