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 > > >