ICTS:34424

Outlier eigenvalues and eigenvectors of generalized Wigner matrices with finite-rank perturbations

(2026). Outlier eigenvalues and eigenvectors of generalized Wigner matrices with finite-rank perturbations. SciVideos. https://scivideos.org/icts-tifr/34424

Outlier eigenvalues and eigenvectors of generalized Wigner matrices with finite-rank perturbations. SciVideos, Apr. 16, 2026, https://scivideos.org/icts-tifr/34424 

          @misc{ scivideos_ICTS:34424,
            doi = {},
            url = {https://scivideos.org/icts-tifr/34424},
            author = {},
            keywords = {},
            language = {en},
            title = {Outlier eigenvalues and eigenvectors of generalized Wigner matrices with finite-rank perturbations},
            publisher = {},
            year = {2026},
            month = {apr},
            note = {ICTS:34424 see, \url{https://scivideos.org/icts-tifr/34424}}
          }
Arijit Chakrabarty
Talk numberICTS:34424
Source RepositoryICTS-TIFR
Collection

Abstract

In this work, a generalized Wigner matrix perturbed by a finite-rank deterministic matrix is studied. The goal is to understand the fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors. Under certain assumptions on the perturbation and the matrix structure, we derive the first-order behavior of these eigenvalues and show that they are well separated from the bulk. The fluctuations of these eigenvalues are shown to follow a multivariate Gaussian distribution, and the asymptotic behavior of the associated eigenvectors is also studied. Central limit theorems that describe the asymptotic alignment of these eigenvectors with the perturbation's eigenvectors, as well as their Gaussian fluctuations around the origin for the non-aligned components, are proven. Furthermore, the convergence of the eigenvector process in a Sobolev space framework is discussed.

This is a joint work with Bishakh Bhattacharya and Rajat Subhra Hazra.