On the Complex Asymptotics of the HCIZ and BGW Integrals

Understand

In this paper, we prove a longstanding conjecture on the asymptotic behavior of a pair of oscillatory matrix integrals: the Harish-Chandra/Itzykson-Zuber (HCIZ) integral, and the Brezin-Gross-Witten (BGW) integral.

• The main result gives a complete asymptotic expansion of these integrals for small complex parameters.
• The coefficients of these asymptotic expansions are generating functions for monotone Hurwitz numbers sorted by genus.