{"_id":"1881","status":"public","quality_controlled":"1","publication_status":"published","volume":164,"issue":"1-2","department":[{"_id":"LaEr"}],"type":"journal_article","date_published":"2016-02-01T00:00:00Z","title":"Extremal eigenvalues and eigenvectors of deformed Wigner matrices","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"}],"scopus_import":1,"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.","date_created":"2018-12-11T11:54:31Z","citation":{"ista":"Lee J, Schnelli K. 2016. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 164(1–2), 165–241.","ieee":"J. Lee and K. Schnelli, “Extremal eigenvalues and eigenvectors of deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 164, no. 1–2. Springer, pp. 165–241, 2016.","apa":"Lee, J., &#38; Schnelli, K. (2016). Extremal eigenvalues and eigenvectors of deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-014-0610-8\">https://doi.org/10.1007/s00440-014-0610-8</a>","mla":"Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 164, no. 1–2, Springer, 2016, pp. 165–241, doi:<a href=\"https://doi.org/10.1007/s00440-014-0610-8\">10.1007/s00440-014-0610-8</a>.","chicago":"Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00440-014-0610-8\">https://doi.org/10.1007/s00440-014-0610-8</a>.","ama":"Lee J, Schnelli K. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2016;164(1-2):165-241. doi:<a href=\"https://doi.org/10.1007/s00440-014-0610-8\">10.1007/s00440-014-0610-8</a>","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241."},"month":"02","author":[{"first_name":"Jioon","last_name":"Lee","full_name":"Lee, Jioon"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"year":"2016","language":[{"iso":"eng"}],"date_updated":"2021-01-12T06:53:49Z","day":"01","publist_id":"5215","intvolume":"       164","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7057"}],"doi":"10.1007/s00440-014-0610-8","ec_funded":1,"publication":"Probability Theory and Related Fields","page":"165 - 241","oa_version":"Preprint","publisher":"Springer","abstract":[{"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&gt;λ+. In particular, the largest eigenvalue of H has a Weibull distribution in the limit N→∞ if λ&gt;λ+. Moreover, for N sufficiently large, we show that the eigenvectors associated to the largest eigenvalues are partially localized for λ&gt;λ+, while they are completely delocalized for λ&lt;λ+. Similar results hold for the lowest eigenvalues. ","lang":"eng"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1}