Uniform in time propagation of chaos for the 2D vortex model and other singular stochastic systems

TL;DR

This paper proves uniform in time propagation of chaos for 2D vortex models and similar singular stochastic systems, extending previous work to include the Biot-Savart kernel on the torus.

Contribution

It adapts existing methods to establish uniform in time propagation of chaos for singular interaction kernels, including the 2D vortex model.

Findings

First uniform in time propagation of chaos result for these systems

Includes models with Biot-Savart kernel on the torus

Extends the applicability of previous propagation of chaos results

Abstract

In this article, we adapt the work of Jabin and Wang (2018) to show the first result of uniform in time propagation of chaos for a class of singular interaction kernels. In particular, our models contain the Biot-Savart kernel on the torus and thus the 2D vortex model.