[{"status":"public","article_number":"e96","month":"10","date_created":"2023-01-12T12:07:30Z","isi":1,"intvolume":"        10","article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2023-01-24T10:02:40Z","volume":10,"abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"publication_status":"published","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"_id":"12148","oa":1,"ddc":["510"],"publication":"Forum of Mathematics, Sigma","title":"Rank-uniform local law for Wigner matrices","year":"2022","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"quality_controlled":"1","citation":{"mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>"},"scopus_import":"1","publication_identifier":{"issn":["2050-5094"]},"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"file":[{"file_name":"2022_ForumMath_Cipolloni.pdf","checksum":"94a049aeb1eea5497aa097712a73c400","access_level":"open_access","success":1,"date_updated":"2023-01-24T10:02:40Z","file_id":"12356","creator":"dernst","content_type":"application/pdf","file_size":817089,"relation":"main_file","date_created":"2023-01-24T10:02:40Z"}],"external_id":{"isi":["000873719200001"]},"date_published":"2022-10-27T00:00:00Z","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","has_accepted_license":"1","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"doi":"10.1017/fms.2022.86","ec_funded":1,"day":"27","oa_version":"Published Version","date_updated":"2023-08-04T09:00:35Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No"},{"publication_identifier":{"issn":["2050-5094"]},"arxiv":1,"date_published":"2018-05-31T00:00:00Z","file":[{"access_level":"open_access","checksum":"5a71b24ba712a3eb2e46165a38fbc30a","file_name":"2018_ForumMahtematics_Akopyan.pdf","file_id":"6356","date_updated":"2020-07-14T12:47:28Z","creator":"dernst","content_type":"application/pdf","file_size":249246,"date_created":"2019-04-30T06:14:58Z","relation":"main_file"}],"external_id":{"arxiv":["1712.10205"],"isi":["000433915500001"]},"language":[{"iso":"eng"}],"doi":"10.1017/fms.2018.7","has_accepted_license":"1","department":[{"_id":"UlWa"},{"_id":"HeEd"},{"_id":"JaMa"}],"ec_funded":1,"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","day":"31","type":"journal_article","date_updated":"2023-09-19T14:50:12Z","oa_version":"Published Version","isi":1,"intvolume":"         6","article_number":"e7","status":"public","date_created":"2019-04-30T06:09:57Z","month":"05","volume":6,"publisher":"Cambridge University Press","file_date_updated":"2020-07-14T12:47:28Z","oa":1,"ddc":["510"],"related_material":{"record":[{"id":"8156","relation":"dissertation_contains","status":"public"}]},"_id":"6355","publication":"Forum of Mathematics, Sigma","title":"Any cyclic quadrilateral can be inscribed in any closed convex smooth curve","publication_status":"published","abstract":[{"lang":"eng","text":"We  prove  that  any  cyclic  quadrilateral  can  be  inscribed  in  any  closed  convex C1-curve.  The smoothness condition is not required if the quadrilateral is a rectangle."}],"project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"quality_controlled":"1","author":[{"first_name":"Arseniy","last_name":"Akopyan","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"id":"3827DAC8-F248-11E8-B48F-1D18A9856A87","full_name":"Avvakumov, Sergey","last_name":"Avvakumov","first_name":"Sergey"}],"citation":{"mla":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>, vol. 6, e7, Cambridge University Press, 2018, doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>.","apa":"Akopyan, A., &#38; Avvakumov, S. (2018). Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>","ista":"Akopyan A, Avvakumov S. 2018. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. Forum of Mathematics, Sigma. 6, e7.","chicago":"Akopyan, Arseniy, and Sergey Avvakumov. “Any Cyclic Quadrilateral Can Be Inscribed in Any Closed Convex Smooth Curve.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2018. <a href=\"https://doi.org/10.1017/fms.2018.7\">https://doi.org/10.1017/fms.2018.7</a>.","short":"A. Akopyan, S. Avvakumov, Forum of Mathematics, Sigma 6 (2018).","ama":"Akopyan A, Avvakumov S. Any cyclic quadrilateral can be inscribed in any closed convex smooth curve. <i>Forum of Mathematics, Sigma</i>. 2018;6. doi:<a href=\"https://doi.org/10.1017/fms.2018.7\">10.1017/fms.2018.7</a>","ieee":"A. Akopyan and S. Avvakumov, “Any cyclic quadrilateral can be inscribed in any closed convex smooth curve,” <i>Forum of Mathematics, Sigma</i>, vol. 6. Cambridge University Press, 2018."},"year":"2018","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}}]