We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels, including the Biot-Savart law. The result applies to the point vortex model approximating the 2D incompressible Navier- Stokes equation and the 2D Euler equation. The method relies on the martingale approach, the Donsker-Varadhan variational formula, and combinatorics techniques. This talk is my recent joint work with Zhenfu Wang and Rongchan Zhu.

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