非厄米型随机矩阵与KP及其相关可积系列

There are close relations between random matrices and integrable system. But people are only concentrating their attention on the research of the Hermitian random matrices, while the research of the non-Hermitian random matrices is comparatively too little. This project will aim at the research of the relations between non-Hermitian random matrices and KP integrable system, including Virasoro constraints, the relation between partition functions and tau functions, and also some KP integrable structures in the non-Hermitian random matrices.

随机矩阵模型与可积系统具有密切联系，但是其研究主要集中在厄米型的随机矩阵模型，而对非厄米型矩阵模型的研究相对较少。本项目拟针对非厄米型矩阵模型与KP可积系统之间的关系展开研究，主要研究Virasoro约束，配分函数和tau函数的关系，以及非厄米型随机矩阵模型中一些与KP相关的可积结构.

随机矩阵模型与可积系统具有密切联系，本项目主要针对非厄米随机矩阵模型与 KP 可积系统之间的关系开展研究，主要研究了KP及其相关可积系列的规范变换，附加对称和平方本征函数对称，对随机矩阵也做了一定的探讨。