We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

中文翻译：

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广义Euler方程点涡的极限定理和涨落。

我们证明了在正温度平衡下二维圆环上的点涡旋系统的平均场极限，大数定律和中心极限定理。点涡旋是推广Euler方程的一类方程的形式解，并且在文献中也被称为广义无粘性SQG。平均场极限是方程的稳定解，CLT极限是方程的平稳分布。