Giovanni Felder, Jens Hoppe, “Orthogonal Polynomials with Complex Densities and Quantum Minimal Surfaces”, SIGMA, 2025, Volume 21,103, 13 pp.

Orthogonal Polynomials with Complex Densities and Quantum Minimal Surfaces

Giovanni Felder^a, Jens Hoppe^b

^a Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
^b Technische Universität Braunschweig, Germany

Abstract: We show that the discrete Painlevé-type equations arising from quantum minimal surfaces are equations for recurrence coefficients of orthogonal polynomials for indefinite hermitian products. As a consequence, we obtain an explicit formula for the initial conditions leading to positive solutions.

Keywords: orthogonal polynomials, quantum minimal surfaces, random matrices, Painlevé equations.

MSC: 33C45, 34M55, 53A10, 15B52

Received: September 1, 2025; in final form November 26, 2025; Published online December 7, 2025

Language: English

DOI: 10.3842/SIGMA.2025.103