MSRI - From Oscillatory Integrals to a Cubic Random Matrix Model"


Location: Bakerboard Room
Abstract:
In this talk I will present some results on complex orthogonal polynomials that 
arise in the application of Gaussian quadrature to certain integrals obtained by
the classical method of steepest descent. The zeros of these complex orthogonal
polynomials are optimal nodes for the computation of oscillatory integrals with
high order stationary points defined on the real axis. In the case of a cubic-type
potential, it is possible to analyze the asymptotic behavior of these orthogonal
polynomials and their zeros by using Riemann-Hilbert techniques. Similar ideas can 
be used to study the partition function and the free energy of the corresponding cubic 
random matrix model. (Joint and ongoing work with P. Bleher, D. Huybrechs, A. B. J. Kuijlaars)