# 대칭 난수 행렬의 고유값 분포

대칭 연속 모수 분포를 사용하여 생성된 대칭 난수 행렬의 고유값을 WignerSemicircleDistribution에 적합 시킵니다.
 In[1]:= XRandomSymmetricMatrix[dist_, n_] := Module[{mat = RandomVariate[dist, {n, n}]}, UpperTriangularize[mat, 1] + Transpose[UpperTriangularize[mat]] ]
 In[2]:= Xdists = {NormalDistribution[], StudentTDistribution[4], LaplaceDistribution[0, 1], WignerSemicircleDistribution[3]}; ev = Eigenvalues[RandomSymmetricMatrix[#, 10^3]] & /@ dists; edist = EstimatedDistribution[#, WignerSemicircleDistribution[r]] & /@ ev;
 In[3]:= Xh[dist_, data_, i_] := Histogram[data, 20, "PDF", ChartStyle -> (ColorData["Gradients"][[RandomInteger[{1, 51} ] ]]), BaseStyle -> {FontFamily -> "Verdana"}, PlotLabel -> dists[[i]], PlotRange -> {0, 1.5 PDF[dist, 0]}, ImageSize -> 280, Epilog -> Inset[Framed[ Style[Grid[{{"Estimated Distribution:"}, {dist}}], 10], RoundingRadius -> 10, FrameStyle -> GrayLevel@0.3, Background -> LightOrange], {Right, 1.45 PDF[dist, 0]}, {Right, Top}]] distPlot[dist_, data_] := Plot[PDF[dist, x], {x, Min[data], Max[data]}, PlotStyle -> {Thick, Black}]
 In[4]:= XGrid[Partition[ Table[Show[h[edist[[i]], ev[[i]], i], distPlot[edist[[i]], ev[[i]]]], {i, 4}], 2]]
 Out[4]=