Novel method for generating long-range correlations

We propose an algorithm to generate a sequence of numbers with long-range power-law correlations which is well-suited for large systems. Starting with a set of random uncorrelated variables, we modify its Fourier transform to get a new sequence with long-range correlations. By mapping the variables to a one dimensional random walk problem we find analytical and numerical evidence of the existence of correlations in the whole system. We exemplify the method by applying it to a generalized percolation problem where the occupancy variables are generated from a long-range correlated sequence.