LARGE N ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS FROM INTEGRABILITY TO ALGEBRAIC GEOMETRY

摘要

We have shown how the asymptotics of orthogonal polynomials (a notion related to integrability) is deeply related to algebraic geometry. This calculation can easily be extended to many generalizations, for multi-matrix models, non-hermitean matrices (β = 1,4), rational potentials,...