A novel method of generating initial conditions for cosmological simulations based on the filtering of white noise is proposed. It is shown that it is possible to obtain any desired zero-mean Gaussian stochastic process (GSP) by applying an appropriate filter to a white-noise (i.e., correlation-free) process. Since instances of white noise processes are easy to generate in practice from standard random number generators, it is therefore possible to create instances of arbitrary GSPs using only a random number generator and a convolution. The convolution may be carried out in a time proportional to M log N using a fast method based on tree codes. This method is distinguished from other methods based on Fourier transforms in that it allows one to sample GSPs with arbitrary sets of window functions, so it may be used to initialize numerical experiments with information at multiple length scales, or with non-cubic lattices. Furthermore, it is shown that instances of constrained GSPs may be obtained from instances of unconstrained processes by another simple filtering process. The filter in this case is local and requires no algorithmic trickery to run in O(N) time, making it far simpler than other proposed methods. The latter technique is independent of the method used to create the unconstrained process.
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