关于HCIZ和BGW积分的复渐近性
On the Complex Asymptotics of the HCIZ and BGW Integrals
摘要：
本文证明了一个关于一对振荡矩阵积分：Harish-Chandra/Itzykson-Zuber（HCIZ）积分和Brezin-Gross-Witten（BGW）积分的渐近性的长期猜想.主要结果给出了小复参数下这些积分的完全渐近展开。这些渐近展开的系数是按亏格排序的单调Hurwitz数的生成函数。
英文摘要：
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.
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