  We consider the Mean Field limit of Gibbsian ensembles of 2-dimensional point
vortices on the torus. It is a classical result that in such limit correlations
functions converge to 1, that is, point vortices decorrelate: we compute the
rate at which this convergence takes place by means of Gaussian integration
techniques, inspired by the correspondence between the 2-dimensional Coulomb
gas and the Sine-Gordon Euclidean field theory.
