Eduardo Chavez Heredia

Degenerate orthogonal polynomials and the Stieltjes-Fekete equilibrium problem

An elegant result dating back to Stieltjes characterises the roots of the classical orthogonal polynomials as points on the line that minimize a suitable potential with logarithmic interactions under an external field. In this talk we review this classical result and introduce the notion of non-Hermitian degenerate orthogonal polynomials (DOP), which are orthogonal polynomials satisfying an excess of orthogonality relations. We then generalise the result of Stieltjes to show that the roots of DOPs solve the Stieltjes-Bethe equations, which determine the equilibrium property of a logarithmic energy functional when the derivative of the external field is a rational function. This talk is based on joint work with Tamara Grava and Marco Bertola.

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/a9bd2e9aec4142178864aa354896ee201d