随机矩阵的双标度极限与极小（2 m，1）模型：退化情形下两截的合并
Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
摘要：
本文证明了随机矩阵模型的双标度极限关联函数在两个割集合并为退化$2m$时（即当整数$m$为任意值时，即当$y\sim x^{2m}$时）与共形$(2m,1)$模型的行列式公式相同.我们的方法遵循Bergère和Eynard在\cite{BergereEynard}中开发的方法，并使用Bleher和Eynard在\cite{BleherEynard}中建议的共形$(2m,1)$模型的Lax对表示（给出Painlevé II可积层次）。特别是，我们定义的贝克-Akhiezer功能相关联的Lax对构建一个内核，然后用于计算行列式公式给出的关联函数的双标度极限的矩阵模型附近的合并两个削减。
英文摘要：
In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Bergère and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlevé II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.
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