{"abstract":[{"lang":"eng","text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395)."}],"oa":1,"year":"2020","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"page":"101-146","language":[{"iso":"eng"}],"day":"16","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"article_processing_charge":"No","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. 2020;1(1):101-146. doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146."},"title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","intvolume":"         1","publication_identifier":{"issn":["2690-1005","2690-0998"]},"scopus_import":"1","quality_controlled":"1","date_published":"2020-11-16T00:00:00Z","volume":1,"publisher":"Mathematical Sciences Publishers","external_id":{"arxiv":["1908.01653"]},"date_created":"2024-03-04T10:27:57Z","month":"11","publication_status":"published","issue":"1","publication":"Probability and Mathematical Physics","oa_version":"Preprint","doi":"10.2140/pmp.2020.1.101","department":[{"_id":"LaEr"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-03-04T10:33:15Z","type":"journal_article","acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","ec_funded":1,"_id":"15063","keyword":["General Medicine"],"status":"public","article_type":"original"}