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RE: Confused about correlations in sequence of Random[] numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg73058] RE: [mg73037] Confused about correlations in sequence of Random[] numbers
• From: "Owen, HL \(Hywel\)" <h.l.owen at dl.ac.uk>
• Date: Wed, 31 Jan 2007 00:44:50 -0500 (EST)

Actually, I worked out why, but it's a useful exercise in understanding
random numbers maybe...

Hywel 

> -----Original Message-----
> From: Owen, HL (Hywel) [mailto:h.l.owen at dl.ac.uk] 
> Sent: 30 January 2007 12:08
> To: mathgroup at smc.vnet.net
> Subject: [mg73037] 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
> 
> 
>