报告题目：Outliers for deformed inhomogeneous random matrices
报 告 人：刘党政 副教授 中国科学技术大学
报告时间：2024年8月15日 10:00-11:00
报告地点： 数学楼 第二报告厅
校内联系人：张勇 zyong2661@jlu.edu.cn
报告摘要：
Inhomogeneous random matrices with a non-trivial variance profile determined by a symmetric stochastic matrix and with independent symmetrically sub-Gaussian entries up to Hermitian symmetry, include many prominent examples, such as remarkable sparse Wigner matrices and random band matrices in dimension d, and have been of great interest recently. In this talk, we study low-rank additive perturbations of such random matrices, and establish a sharp BBP phase transition for extreme eigenvalues at the level of law of large numbers. Under suitable conditions on the variance profile and the finite-rank perturbation, we also establish the fluctuations of spectral outliers that may be characterized by the general inhomogeneous random matrices. This reveals the strong non-universality phenomena, which may depend on eigenvectors, sparsity or geometric structure.
报告人简介：
刘党政, 中国科学技术大学副教授，研究兴趣随机矩阵理论与应用, 已在Comm. Math. Phys., Int. Math. Res. Notices, AIHP（B)等杂志上发表论文多篇。
