Map Enumeration and the Asymptotics of Orthogonal Polynomial Recurrence Coefficients
When
12:30 p.m., Sept. 8, 2020
In this talk we will take a dynamical systems perspective, in order to analyze the recurrence coefficients for orthogonal polynomials prescribed by integration against the exponential of an even polynomial. Using several different asymptotic expansions for these recurrence coefficients, we obtain rigorous approximations for these coefficients in different parameter regimes. Together, these expansions also enable us to solve for the generating functions of labeled maps on a genus g Riemann surface.