This note studies the deterministic flow of measures which is the limiting case as n → ∞ of Dyson's model of the motion of the eigenvalues of random symmetric n × n matrices. Though this flow is nonlinear, highly singular and apparently of Wiener-Hopf type, it may be solved explicitly without recourse to Wiener-Hopf theory. The solution greatly clarifies the role of the famous Wigner semicircle law.
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Terence Chan (1994) studied this question.