CONSTRAINED REALIZATIONS OF GAUSSIAN FIELDS - A SIMPLE ALGORITHM

We present a straightforward method for the construction of constrained realizations of Gaussian fields. Consider a Gaussian random field and its ensemble mean field given a set of constraints. The residual of the field from its mean is statistically independent of the actual numerical value of the constraints. The algorithm is based on a simple construction of this residual field, which is then added to the analytically calculated mean field. This algorithm is exact and involves no iterations. The computational effort involves only setting one random realization in the inverse k-space, its FFT to real space, and the calculation of the mean field (given the set of constraints) over all grid points. Furthermore, it can be applied to a large number of constraints of arbitrary amplitudes and positions. The algorithm facilitates the generation of the initial conditions for N-body simulations which obey a few hundreds of constraints imposed by the observable universe.