The isomonodromy approach to matrix models in 2D quantum gravity (Q1200498)

The analysis performed in this article complements the isomonodromy approach, proposed by \textit{G. Moore} [NATO ASI Ser., Ser. B 262, 157-190 (1991)], to the general string equations that come from the matrix model in the continuous limit and is original by the fact that the isomonodromy technique is applied to investigate the double-scaling limit itself. Based on the WKB-analysis of the \(L-A\) pairs corresponding to the discrete string equation, the authors consider the double-scaling limit in the Hermitian matrix model for 2D quantum gravity associated with the measure \(\exp(t_ jz^{2j})\) for \(N3\), concretely show that the Cross- Migdal-Douglas-Shenker limit to the Painlevé I equation is valid after an appropriate modification of the contour of integration and calculate the nonperturbative parameters of the corresponding Painlevé function.