1月17日 李韫博士学术报告(数学与统计学院)

文章作者:  发布时间: 2024-01-15  浏览次数: 10

报 告 人:李韫 博士

报告题目: Edge imits of the truncated circular beta ensembles

报告时间:2024年1月17日(周三)上午10:00-11:00

报告地点:静远楼1709学术报告厅

报告人简介:

       李韫,清华大学丘成桐数学科学中心博士后。本科毕业于南开大学,博士毕业于美国威斯康星大学麦迪逊分校,导师为Benedek Valko教授。研究领域为随机矩阵,具体研究的问题包括高维随机矩阵的谱分析和Beta系综的极限等问题。

报告摘要:

       Consider the circular unitary ensemble with the first row and column deleted, the resulting model is sub-unitary with eigenvalues lying inside the unit disk. Zyczkowski and Sommers derived the joint eigenvalue distribution of a truncated circular unitary ensemble, and showed they form a determinantal point process. Taking the limit of these points (without any additional scaling) one obtains the zeros of the Gaussian analytic function studied by Peres and Virag.  

       Killip and Kozhan provided a random matrix model that can be considered as the truncated circular beta ensemble (with beta = 2 corresponding to the unitary case), and described the spectrum via a random recursion. We derive and describe the point process limit of the truncated circular beta ensemble (near 1) together with the scaling limit of the normalized characteristic polynomials. We also treat multiplicative rank one perturbation of the models. The limiting objects are closely connected to the random analytic function appearing as the limit of the normalized characteristic polynomials of the (full) circular beta ensemble. Based on joint work with Benedek Valko.