论文标题
在HCIZ和BGW积分的复杂渐近学上
On the Complex Asymptotics of the HCIZ and BGW Integrals
论文作者
论文摘要
在本文中，我们证明了对一对振荡矩阵积分的渐近行为的长期猜想：Harish-Chandra/Itzykson-Zuber（HCIZ）积分和Brezin-Gross-witter（BGW）积分。主要结果为这些积分提供了针对小型复杂参数的完整渐近扩展。这些渐近扩展的系数是为单酮hurwitz数字产生的功能。
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.
