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The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"}],"oa_version":"Published Version","quality_controlled":"1","publication_status":"published","citation":{"apa":"Bossmann, L., Petrat, S. P., &#38; Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>","ieee":"L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021.","chicago":"Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.22\">https://doi.org/10.1017/fms.2021.22</a>.","ama":"Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>","mla":"Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e28, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.22\">10.1017/fms.2021.22</a>.","short":"L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021).","ista":"Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28."},"abstract":[{"text":"We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.","lang":"eng"}],"author":[{"id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","last_name":"Bossmann","full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","first_name":"Lea"},{"id":"40AC02DC-F248-11E8-B48F-1D18A9856A87","last_name":"Petrat","full_name":"Petrat, Sören P","orcid":"0000-0002-9166-5889","first_name":"Sören P"},{"first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}]},{"has_accepted_license":"1","department":[{"_id":"LaEr"}],"date_created":"2021-06-13T22:01:33Z","file":[{"date_updated":"2021-06-15T14:40:45Z","access_level":"open_access","date_created":"2021-06-15T14:40:45Z","checksum":"47c986578de132200d41e6d391905519","file_name":"2021_ForumMath_Bao.pdf","file_size":483458,"creator":"cziletti","file_id":"9555","content_type":"application/pdf","relation":"main_file","success":1}],"month":"05","article_type":"original","date_published":"2021-05-27T00:00:00Z","scopus_import":"1","publisher":"Cambridge University Press","language":[{"iso":"eng"}],"publication":"Forum of Mathematics, Sigma","file_date_updated":"2021-06-15T14:40:45Z","day":"27","type":"journal_article","intvolume":"         9","status":"public","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"e44","isi":1,"ddc":["510"],"year":"2021","doi":"10.1017/fms.2021.38","ec_funded":1,"title":"Equipartition principle for Wigner matrices","external_id":{"arxiv":["2008.07061"],"isi":["000654960800001"]},"arxiv":1,"article_processing_charge":"No","volume":9,"oa":1,"date_updated":"2023-08-08T14:03:40Z","publication_identifier":{"eissn":["20505094"]},"_id":"9550","project":[{"grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","citation":{"mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. 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"}],"author":[{"first_name":"Zhigang","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}]},{"ec_funded":1,"year":"2020","doi":"10.1017/fms.2020.17","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","external_id":{"isi":["000527342000001"],"arxiv":["1910.03372"]},"article_number":"e20","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"related_material":{"record":[{"status":"public","id":"7524","relation":"earlier_version"}]},"citation":{"chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","ista":"Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20.","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>.","ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>"},"publication_status":"published","author":[{"full_name":"Deuchert, Andreas","last_name":"Deuchert","orcid":"0000-0003-3146-6746","first_name":"Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"},{"id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon","last_name":"Mayer","first_name":"Simon"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert"}],"abstract":[{"lang":"eng","text":"We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 ."}],"article_processing_charge":"No","date_updated":"2023-08-21T06:18:49Z","volume":8,"oa":1,"arxiv":1,"oa_version":"Published Version","quality_controlled":"1","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["20505094"]},"_id":"7790","date_published":"2020-03-14T00:00:00Z","article_type":"original","month":"03","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Cambridge University Press","department":[{"_id":"RoSe"}],"has_accepted_license":"1","file":[{"date_updated":"2020-07-14T12:48:03Z","access_level":"open_access","file_name":"2020_ForumMath_Deuchert.pdf","file_size":692530,"date_created":"2020-05-04T12:02:41Z","checksum":"8a64da99d107686997876d7cad8cfe1e","content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"7797"}],"date_created":"2020-05-03T22:00:48Z","type":"journal_article","day":"14","status":"public","intvolume":"         8","file_date_updated":"2020-07-14T12:48:03Z","publication":"Forum of Mathematics, Sigma"},{"article_type":"original","date_published":"2019-03-26T00:00:00Z","month":"03","language":[{"iso":"eng"}],"publisher":"Cambridge University Press","scopus_import":"1","department":[{"_id":"LaEr"}],"has_accepted_license":"1","file":[{"date_updated":"2020-07-14T12:47:22Z","access_level":"open_access","file_name":"2019_Forum_Erdoes.pdf","file_size":1520344,"date_created":"2019-09-17T14:24:13Z","checksum":"933a472568221c73b2c3ce8c87bf6d15","content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"6883"}],"date_created":"2019-03-28T09:05:23Z","type":"journal_article","day":"26","status":"public","intvolume":"         7","file_date_updated":"2020-07-14T12:47:22Z","publication":"Forum of Mathematics, Sigma","ec_funded":1,"year":"2019","doi":"10.1017/fms.2019.2","title":"Random matrices with slow correlation decay","external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"article_number":"e8","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"publication_status":"published","citation":{"ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>.","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press, 2019.","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>."},"author":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"abstract":[{"lang":"eng","text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."}],"date_updated":"2023-09-07T12:54:12Z","oa":1,"volume":7,"article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"}],"quality_controlled":"1","_id":"6182","publication_identifier":{"eissn":["20505094"]}}]