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

TL;DR

This paper derives a stochastic 2D vortex model from particle systems with moderate interactions, providing quantitative estimates using advanced probabilistic and analytical techniques.

Contribution

It introduces a novel combination of Fisher information control, inequalities, and localization methods to analyze the nonlinear stochastic vortex model on the whole space.

Findings

Quantitative estimates in entropy and energy functionals for the particle system.

Construction of a suitable solution for the limiting stochastic vortex process.

Integration of Fisher information control with Ladyzhenskaya and Donsker-Varadhan inequalities.

Abstract

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.