Orthogonal Polynomials with Complex Densities and Quantum Minimal Surfaces - Felder, Giovanni; Hoppe, Jens (Symmetry, Integrability and Geometry: Methods and Applications, 2025)
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.