Commuting difference operators, spinors on hyperelliptic curves and
asymptotics of generalized orthogonal polynomials: Part II"
Speaker: M. Bertola
Abstract
We show how to use the inverse spectral problem and the theory of
commuting difference operators to obtain heuristics for the
asymptotics of
orthogonal polynomials for large degrees (and varying complex
weight). The
formulas are proven correct by Part I using a rigorous Its-Deift- Zhou
steepest descent argument based on the notion of admissible
Boutroux
curve.
We show how to construct such curves and harmonic functions in
complete
generality using the notion of "welding" of surfaces developed in
the
theory of quadratic differentials by Strebel and used in a
different
context to parametrize the moduli spaces of smooth curves with
marked
points.