Confused about correlations in sequence of Random[] numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg73037] Confused about correlations in sequence of Random[] numbers*From*: "Owen, HL \(Hywel\)" <h.l.owen at dl.ac.uk>*Date*: Tue, 30 Jan 2007 07:08:21 -0500 (EST)

Hi folks, I'm confused about what this all means. First, I make a list of Uniformly-distributed random numbers. Then I make copies of this list rotated by n,2n,3n,4n... and I make m copies. I then add the numbers together, and look at these values and their Fourier transform. The whole thing is done like this: list1 = Table[Random[], {1000}]; lists = Table[RotateLeft[list1, 8n], {n, 1, 20}]; olist = Plus @@ lists; ListPlot[olist, PlotJoined -> True]; ListPlot[Re[Fourier[olist]], PlotJoined -> True, AxesOrigin -> {0, 0}]; I see very strong correlations, but I don't understand why. Can anyone give me a simple explanation? I'm sure there is one, but I don't see it. Hywel