Double scaling limit for matrix models with nonanalytic potentials
Double scaling limit for matrix models with nonanalytic potentials
复制标题
具有非解析势的矩阵模型的双标度限制
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. Shcherbina
中科院分区：
文献类型：
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作者：
M. Shcherbina
我们研究具有非解析势的随机矩阵的酉不变系综的双标度极限，并找到相应雅可比矩阵条目的渐近展开式。我们的方法基于弦方程的微扰展开。雅可比矩阵系数的一阶微扰项通过 Painleve II 方程的 Hastings-McLeod 解来表达。极限再现核用狄拉克微分方程组的解来表达，其势由展开式的一阶项定义。
We study the double scaling limit for unitary invariant ensembles of random matrices with nonanalytic potentials and find the asymptotic expansion for the entries of the corresponding Jacobi matrix. Our approach is based on the perturbation expansion for the string equations. The first order perturbation terms of the Jacobi matrix coefficients are expressed through the Hastings–McLeod solution of the Painleve II equation. The limiting reproducing kernel is expressed in terms of solutions of the Dirac system of differential equations with a potential defined by the first order terms of the expansion.