Speaker: 刘党政，中国科学技术大学

Inviter: 随机分析研究中心

Title: Outliers for deformed inhomogeneous random matrices

Language: Chinese

Time & Venue: 2025.07.04 16:00-17:00 南楼613

Abstract: Inhomogeneous random matrices with a non-trivial variance profile determined by a symmetric Markov matrix and with independent symmetrically sub-Gaussian entries up to Hermitian symmetry, include many prominent examples, such as Wigner matrices, remarkable sparse Wigner matrices and random band matrices, 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. Based on joint work with Ruohan Geng and Guangyi Zou.