{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T07:47:32Z","timestamp":1791445652889,"version":"4.3.3"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:00:00Z","timestamp":1672358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"publisher","award":["EP\/V002473\/1"],"award-info":[{"award-number":["EP\/V002473\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Complex eigenvalues of random matrices J=GUE+i\u03b3diag(1,0,\u2026,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N\u226b1 the eigenvalue density of J undergoes an abrupt restructuring at \u03b3=1, the critical threshold beyond which a single eigenvalue outlier (\u201cbroad resonance\u201d) appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold \u03b3=1 and the associated scaling for the real parts (\u201cresonance positions\u201d) and imaginary parts (\u201cresonance widths\u201d) of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function.<\/jats:p>","DOI":"10.3390\/e25010074","type":"journal-article","created":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T04:17:38Z","timestamp":1672633058000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Extreme Eigenvalues and the Emerging Outlier in Rank-One Non-Hermitian Deformations of the Gaussian Unitary Ensemble"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4091-892X","authenticated-orcid":false,"given":"Yan V.","family":"Fyodorov","sequence":"first","affiliation":[{"name":"Department of Mathematics, King\u2019s College London, London WC2R 2LS, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6114-4724","authenticated-orcid":false,"given":"Boris A.","family":"Khoruzhenko","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5897-5682","authenticated-orcid":false,"given":"Mihail","family":"Poplavskyi","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1918","DOI":"10.1063\/1.531919","article-title":"Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering: Random matrix approach for systems with broken time-reversal invariance","volume":"38","author":"Fyodorov","year":"1997","journal-title":"J. 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