--- _id: '1881' abstract: - lang: eng text: 'We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i.i.d.\ entries that are independent of W. We assume subexponential decay for the matrix entries of W and we choose λ∼1, so that the eigenvalues of W and λV are typically of the same order. Further, we assume that the density of the entries of V is supported on a single interval and is convex near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such that the largest eigenvalues of H are in the limit of large N determined by the order statistics of V for λ>λ+. In particular, the largest eigenvalue of H has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently large, we show that the eigenvectors associated to the largest eigenvalues are partially localized for λ>λ+, while they are completely delocalized for λ<λ+. Similar results hold for the lowest eigenvalues. ' acknowledgement: "Most of the presented work was obtained while Kevin Schnelli was staying at the IAS with the support of\r\nThe Fund For Math." author: - first_name: Jioon full_name: Lee, Jioon last_name: Lee - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Lee J, Schnelli K. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 2016;164(1-2):165-241. doi:10.1007/s00440-014-0610-8 apa: Lee, J., & Schnelli, K. (2016). Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-014-0610-8 chicago: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer, 2016. https://doi.org/10.1007/s00440-014-0610-8. ieee: J. Lee and K. Schnelli, “Extremal eigenvalues and eigenvectors of deformed Wigner matrices,” Probability Theory and Related Fields, vol. 164, no. 1–2. Springer, pp. 165–241, 2016. ista: Lee J, Schnelli K. 2016. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 164(1–2), 165–241. mla: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 164, no. 1–2, Springer, 2016, pp. 165–241, doi:10.1007/s00440-014-0610-8. short: J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241. date_created: 2018-12-11T11:54:31Z date_published: 2016-02-01T00:00:00Z date_updated: 2021-01-12T06:53:49Z day: '01' department: - _id: LaEr doi: 10.1007/s00440-014-0610-8 ec_funded: 1 intvolume: ' 164' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1310.7057 month: '02' oa: 1 oa_version: Preprint page: 165 - 241 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Probability Theory and Related Fields publication_status: published publisher: Springer publist_id: '5215' quality_controlled: '1' scopus_import: 1 status: public title: Extremal eigenvalues and eigenvectors of deformed Wigner matrices type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2016' ...