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Decay of correlation rate in the mean field limit of point vortices ensembles
Stochastics and Dynamics  (IF0.98),  Pub Date : 2020-08-18, DOI: 10.1142/s0219493720400092
Francesco Grotto, Marco Romito

We consider the Mean Field limit of Gibbsian ensembles of 2-dimensional (2D) 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 2D Coulomb gas and the Sine-Gordon Euclidean field theory.