Peter Elbau
(ETH Zurich)
Random normal matrices and polynomial curves
In the large matrix limit, the eigenvalues of the random matrices for a
somewhat special chosen potential will uniformly fill the interior domain
of a polynomial curve determined by its harmonic moments which enter the
potential as coefficients.
Furthermore, the dispersionless Toda hierarchy fulfilled by polynomial
curves may be recovered as limit of the Toda hierarchy corresponding to
the orthogonal polynomials of the matrix model.