Converting planar orthogonality to orthogonality on a contour

by Alan Groot (KU Leuven)

Location: 200B.02.18, Leuven
Time: Wednesday March 6, 2019 at 10:30

We look at a model related to the spherical ensemble, by introducing two points on the sphere that repel particles. The corresponding average characteristic polynomial satisfies a Hermitian orthogonality on the complex plane. We show how to convert this planar orthogonality to non-Hermitian orthogonality with respect to a weight on a collection of contours. We further show that this collection of contours satisfies a max-min energy problem with respect to an external field. Finally, we derive some properties of the equilibrium measure which generates this energy, both theoretically and numerically (e.g. the support and the density).