Holtsmark distributions in point-vortex systems

The statistics of uncorrelated point vortices in a plane is studied analytically and numerically. Theoretical distributions are obtained with the general method developed by Holtsmark [Ann. Phys. 58, 577 (1919)] and Chandrasekhar [Rev. Mod. Phys. 15, 1 (1943)]. They are found to agree with the results of numerical tests. Randomly placed Euler vortices have neatly Gaussian velocity distributions and Lorentzian distributions of the velocity difference. Statistics of other types of point vortices is essentially non-Gaussian.