Dynamics of the McKean-Vlasov Equation

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.