The eigenvalues of a random matrix behave like interacting particles confined in a potential. The locations of eigenvalues are Not independent.

To observe the dependence of the eigenvalues let's do an experiment. First we take one randomly chosen eigenvalue from a 20 by 20 matrix, and repeat with a new matrix to get 20 independent eigenvalues.

We compare this to all 20 eigenvalues of one matrix.

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