On the Complex Asymptotics of the HCIZ and BGW Integrals
Combinatorics
2020-06-09 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2006.04304,
title = {On the Complex Asymptotics of the HCIZ and BGW Integrals},
author = {Jonathan Novak},
journal= {arXiv preprint arXiv:2006.04304},
year = {2020}
}
Comments
Preliminary version, comments welcome