Establish commutativity of semiclassical and classical limits

Establish a general geometric explanation for the commutativity of the semiclassical double-scaling limit followed by $a\to1$ and the direct $q\to1$ limit at fixed $N$ for the q-Laguerre and q-Gaussian matrix models.

Background

The paper compares two limiting procedures: the semiclassical limit $q\to1$, $N\to\infty$ with $a=q^N$ fixed, and the direct $q\to1$ limit at fixed $N$. Examples show agreement with the large-$N$ expansion of the classical Gaussian matrix model at leading and next-to-leading order, but a general explanation of this agreement is unresolved.