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Wigner’s Semicircle Law — from Wolfram MathWorld

Fat Tails du Jour: Random Matrices do not obey Wigner's semicircle law; effect on #BigData

  • The distribution of eigenvalues of a symmetric random matrix with entries chosen from a standard normal distribution is illustrated above for a random matrix.
  • The law was first observed by Wigner (1955) for certain special classes of random matrices arising in quantum mechanical investigations.
  • SEE ALSO: Eigenvalue , Girko’s Circular Law , Random Matrix

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@nntaleb: “Fat Tails du Jour: Random Matrices do not obey Wigner’s semicircle law; effect on #BigData”


Let be a real symmetric matrix of large order having random
elements that for are independently
distributed with equal densities, equal second moments , and th moments bounded
by constants independent of , , and . Further, let
be the number of
eigenvalues of that lie in the
interval for real . Then


Wigner’s Semicircle Law — from Wolfram MathWorld

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