Primordial Gaussian perturbation fields - Constrained realizations

A novel method is devised in order to impose constraints on simulated realizations of random Gaussian fields. The power spectrum of the residual from the (ensemble) mean field under the given constraints is calculated. The Fourier components of the residual field have amplitudes set by the required power spectrum, and phases which are initially assumed to be uniformly distributed. A simple iterative procedure allows imposing constraints on the residual field while keeping its power spectrum intact. By transforming back and forth between real and Fourier spaces while constraining the field components in both domains, the required realizations are obtained within a few cycles.