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Confused about correlations in sequence of Random[] numbers


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


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