報告題目：Outliers for deformed inhomogeneous random matrices
報 告 人：劉黨政 副教授 中國科學技術大學
報告時間：2024年8月15日 10:00-11:00
報告地點： 數學樓 第二報告廳
校内聯系人：張勇 zyong2661@jlu.edu.cn
報告摘要：
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.
報告人簡介：
劉黨政, 中國科學技術大學副教授，研究興趣随機矩陣理論與應用, 已在Comm. Math. Phys., Int. Math. Res. Notices, AIHP（B)等雜志上發表論文多篇。
