Critical-point screening in random wave fields

Screening of vortices and other critical points in a two-dimensional random Gaussian field is studied by using large-scale computer simulations and analytic theory. It is shown that the topological charge imbalance and its variance in a bounded region can be obtained from signed zero crossings on the boundary of the region. A first-principles Gaussian theory of these zero crossings and their correlations is derived for the vortices and shown to be in good agreement with the computer simulation. An exact relationship is obtained between the variance of the charge imbalance and the charge correlation function, and this relationship is verified by comparison with the data. The results obtained are extended to arbitrarily shaped volumes in isotropic spaces of higher dimension.