Study on stochastic processes with determinantal structure

某些随机矩阵特征值的相关函数可用行列式表示。关联函数为行列式的点组态具有排斥性，称为行列式点过程。许多数学对象都可以用一个决定点过程来描述并进行精确分析。本文研究了Ginibre点过程这一典型的决定点过程模型，并以此决定点过程代替Poisson点过程作为蜂窝网络基站的模型进行了分析，从理论和应用数学的角度对决定点过程进行了研究。

Correlation functions of the eigenvalues of certain random matrices can be expressed by using determinant. A point configuration whose correlation functions are determinants has repulsive property and is called a determinantal point process. Many mathematical objects can be described as a determinantal point process and analyzed precisely. We study the Ginibre point process, which is a typical model of determinantal point process, and we use this determinantal point process instead of poisson point process as a model of base stations of a cellular network and analyze it. We investigated determinantal point processes from both theoretical and applied mathematical points of view.