In[]:=
CompoundExpression[
]
​​deploy
Thu 4 May 2023 00:37:38

Approximating DPR1 eigenvalues

Checking answer of Rainer R on scicomp ?
Spectrum of a large random matrix becomes deterministic, hence use the “canonical” spectrum

Sanity check of Marchenko-Pastur


DPR1 spectrum

In[]:=
ClearAll["Global`*"];​​eigMagnitude=InverseCDF[MarchenkoPasturDistribution[.5],y]/.y->1-x;​​Plot@@{eigMagnitude,{x,0,1},PlotLabel->"random spectrum"}
Out[]=
In[]:=
numSamples=45;​​eigs=Table[eigMagnitude,{x,0,1,1./numSamples}];​​dpr1=Rest@Eigenvalues[-2DiagonalMatrix[eigs]+{eigs}.{eigs}];​​ListPlot[{dpr1,-2Most[eigs],-2Rest[eigs],-Total/@Partition[eigs,2,1]},Filling->{2->{3}},Joined->{True,True,True,False},PlotLegends->{"True","Upper","Lower","Average"}]
Out[]=
True
Upper
Lower
Average
In[]:=
ListPlot[{dpr1+Total/@Partition[eigs,2,1],dpr1+2Most[eigs],dpr1+2Rest[eigs]},Joined->{False,True,True},PlotLegends->{"average","upper","lower"}]
Out[]=
average
upper
lower