In[]:=
deploy
Thu 4 Aug 2022 15:30:40
In[]:=
d=7;​​numSamples=10000;​​sigma=DiagonalMatrix[Table[1,{d}]];​​dist=MultinormalDistribution[sigma];​​data=RandomVariate[dist,numSamples];​​data=Normalize/@data;​​​​getNorm[bsize_]:=Mean[Norm[#]&/@Partition[data,bsize]];​​getRank[bsize_]:=Mean
2
(Norm[#]-1)
(bsize)&/@Partition[data,bsize];​​plot1=ListPlot[Table[getRank[k],{k,2,1000}],PlotRange->All];​​plot2=PlotLabeled1d,"
1
d
",{x,1,1000},PlotStyle->Dashed;​​Show[plot1,plot2]
Out[]=