  In arXiv:1004.1407, Flandoli, Gubinelli, and Priola proposed a stochastic
variant of the classical point vortex system of Helmholtz and Kirchoff in which
multiplicative noise of transport-type is added to the dynamics. An open
problem in the years since is to show that in the mean-field scaling regime, in
which the circulations are inversely proportional to the number of vortices,
the empirical measure of the system converges to a solution of a
two-dimensional Euler vorticity equation with multiplicative noise. By
developing a stochastic extension of the modulated-energy method of Serfaty and
Duerinckx for mean-field limits of deterministic particle systems and by
building on ideas introduced by the author for studying such limits at the
scaling-critical regularity of the mean-field equation, we solve this problem
under minimal assumptions.
