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Here we show how to produce a 3D density field with a given set ofhigher-order correlation functions. Our algorithm enables producing any desiredtwo-point, three-point, and four-point functions, including odd-parity for thelatter. We also outline how to generalize the algorithm to i) N-pointcorrelations with $N>4$, ii) dimensions other than 3, and iii) beyond scalarquantities. This algorithm should find use in verifying analysis pipelines forhigher-order statistics in upcoming galaxy redshift surveys such as DESI,Euclid, Roman, and Spherex, as well as intensity mapping

Algorithm to Produce a Density Field with Given Two, Three, and Four-Point Correlation Functions