{"day":"01","publisher":"Springer Nature","file_date_updated":"2023-01-27T11:06:47Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","abstract":[{"lang":"eng","text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold."}],"isi":1,"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"has_accepted_license":"1","article_type":"original","quality_controlled":"1","external_id":{"isi":["000796323500001"]},"date_published":"2022-11-01T00:00:00Z","article_processing_charge":"No","doi":"10.1007/s00023-022-01188-8","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>"},"intvolume":"        23","title":"Density of small singular values of the shifted real Ginibre ensemble","oa":1,"ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"page":"3981-4002","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","publication":"Annales Henri Poincaré","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"department":[{"_id":"LaEr"}],"status":"public","_id":"12232","scopus_import":"1","oa_version":"Published Version","publication_status":"published","file":[{"relation":"main_file","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","file_size":1333638,"access_level":"open_access","creator":"dernst","date_updated":"2023-01-27T11:06:47Z","date_created":"2023-01-27T11:06:47Z","success":1,"file_id":"12424","content_type":"application/pdf","checksum":"5582f059feeb2f63e2eb68197a34d7dc"}],"month":"11","date_updated":"2023-08-04T09:33:52Z","date_created":"2023-01-16T09:50:26Z","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"year":"2022","volume":23,"issue":"11","language":[{"iso":"eng"}]}