Crossover phenomenon for the largest singular value of the spiked elliptic Ginibre ensemble
报 告 人:: 刘党政
报告地点:: 数学与统计学院415室
报告时间:: 2019年06月18日星期二15:00-16:00

The complex elliptic Ginibre ensemble is a complex Gaussian matrix interpolating between the Gaussian unitary ensemble and the Ginibre ensemble. Its eigenvalues form a determinantal point process in the complex plane, however, until recently singular values have been proved to build a Pfaffian point process by Kanazawa and Kieburg. In this paper we turn to consider an extended elliptic Ginibre ensemble with correlated rows and columns, which connects GUE and the spiked Wishart matrix. We prove that the singular values still build a Pfaffian point process with correlation kernel expressed by a contour integral representation, and further observe a crossover transition of the largest singular value at certain critical value of coupling parameter. Our result, which is given by a Fredholm Pfaffian series expansion, interpolates the distribution of largest eigenvalues of squared GUE and the TW-2 distribution of GUE. Joint work with Yanhui Wang, Henan University.

发 布 人:吴双 发布时间: 2019-06-11
刘党政,2005本科毕业于陕西师范大学数学与信息科学学院,2010博士毕业于北京大学数学科学学院。2010.10-2012.08在智利Universidad de Talca从事博士后研究,2012.09-2015.11在中国科学技术大学数学科学学院任特任副教授,2015.12起任副教授。研究方向为随机矩阵理论,相关论文发表在Comm. Math. Phys., Constr. Approx., Int. Math. Res. Notices, AIHP Probabilités et Statistiques, Electron. J. Probab.等杂志。