The fluctuation behaviour of the stochastic point vortex model with common noise

Abstract: This article studies the fluctuation behaviour of the stochastic point vortex model with common noise. Using the martingale method combined with a localization argument, we prove that the sequence of fluctuation processes converges in distribution to the unique probabilistically strong solution of a linear stochastic evolution equation. In particular, we establish the strong convergence from the stochastic point vortex model with common noise to the conditional McKean Vlasov equation.