[{"intvolume":"         6","volume":6,"type":"journal_article","status":"public","abstract":[{"text":"We consider the confined Fröhlich polaron and establish an asymptotic series for the low-energy eigenvalues in negative powers of the coupling constant. The coefficients of the series are derived through a two-fold perturbation approach, involving expansions around the electron Pekar minimizer and the excitations of the quantum field.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.16373","open_access":"1"}],"language":[{"iso":"eng"}],"page":"281-325","oa_version":"Preprint","article_processing_charge":"No","quality_controlled":"1","article_type":"original","OA_place":"repository","scopus_import":"1","department":[{"_id":"RoSe"}],"date_published":"2025-02-23T00:00:00Z","arxiv":1,"acknowledgement":"M.B. gratefully acknowledges funding from the ERC Advanced Grant ERC-AdG CLaQS, grant agreement n. 83478.","publication_status":"published","issue":"1","oa":1,"date_created":"2025-03-09T23:01:28Z","_id":"19372","day":"23","OA_type":"green","publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"title":" Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling","date_updated":"2025-03-10T07:19:02Z","publisher":"Mathematical Sciences Publishers","corr_author":"1","year":"2025","publication":"Probability and Mathematical Physics","doi":"10.2140/pmp.2025.6.281","author":[{"last_name":"Brooks","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","orcid":"0000-0002-6249-0928","first_name":"Morris"},{"id":"cbddacee-2b11-11eb-a02e-a2e14d04e52d","full_name":"Mitrouskas, David Johannes","last_name":"Mitrouskas","first_name":"David Johannes"}],"month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2306.16373"]},"citation":{"chicago":"Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/pmp.2025.6.281\">https://doi.org/10.2140/pmp.2025.6.281</a>.","ama":"Brooks M, Mitrouskas DJ.  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. <i>Probability and Mathematical Physics</i>. 2025;6(1):281-325. doi:<a href=\"https://doi.org/10.2140/pmp.2025.6.281\">10.2140/pmp.2025.6.281</a>","ista":"Brooks M, Mitrouskas DJ. 2025.  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. Probability and Mathematical Physics. 6(1), 281–325.","apa":"Brooks, M., &#38; Mitrouskas, D. J. (2025).  Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2025.6.281\">https://doi.org/10.2140/pmp.2025.6.281</a>","short":"M. Brooks, D.J. Mitrouskas, Probability and Mathematical Physics 6 (2025) 281–325.","ieee":"M. Brooks and D. J. Mitrouskas, “ Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling,” <i>Probability and Mathematical Physics</i>, vol. 6, no. 1. Mathematical Sciences Publishers, pp. 281–325, 2025.","mla":"Brooks, Morris, and David Johannes Mitrouskas. “ Asymptotic Series for Low-Energy Excitations of the Fröhlich Polaron at Strong Coupling.” <i>Probability and Mathematical Physics</i>, vol. 6, no. 1, Mathematical Sciences Publishers, 2025, pp. 281–325, doi:<a href=\"https://doi.org/10.2140/pmp.2025.6.281\">10.2140/pmp.2025.6.281</a>."}},{"publication_status":"published","issue":"4","oa":1,"date_created":"2024-05-29T06:12:54Z","_id":"17074","day":"21","ec_funded":1,"publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"title":"Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases","date_updated":"2025-04-14T07:26:59Z","publisher":"Mathematical Sciences Publishers","corr_author":"1","year":"2023","publication":"Probability and Mathematical Physics","doi":"10.2140/pmp.2022.3.939","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","full_name":"Brooks, Morris","last_name":"Brooks","first_name":"Morris","orcid":"0000-0002-6249-0928"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","external_id":{"arxiv":["2111.13864"]},"citation":{"ista":"Brooks M, Seiringer R. 2023. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. Probability and Mathematical Physics. 3(4), 939–1000.","ama":"Brooks M, Seiringer R. Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. 2023;3(4):939-1000. doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>","chicago":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>.","mla":"Brooks, Morris, and Robert Seiringer. “Validity of Bogoliubov’s Approximation Fortranslation-Invariant Bose Gases.” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4, Mathematical Sciences Publishers, 2023, pp. 939–1000, doi:<a href=\"https://doi.org/10.2140/pmp.2022.3.939\">10.2140/pmp.2022.3.939</a>.","ieee":"M. Brooks and R. Seiringer, “Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases,” <i>Probability and Mathematical Physics</i>, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 939–1000, 2023.","apa":"Brooks, M., &#38; Seiringer, R. (2023). Validity of Bogoliubov’s approximation fortranslation-invariant Bose gases. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2022.3.939\">https://doi.org/10.2140/pmp.2022.3.939</a>","short":"M. Brooks, R. Seiringer, Probability and Mathematical Physics 3 (2023) 939–1000."},"volume":3,"intvolume":"         3","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by EN=NeH+infσ(H)+oN→∞(1), where N is the number of particles, eH is the minimal Hartree energy and H is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states ΨN, i.e. states satisfying ⟨HN⟩ΨN=EN+oN→∞(1), exhibiting complete Bose--Einstein condensation with respect to one of the Hartree minimizers."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2111.13864","open_access":"1"}],"page":"939-1000","language":[{"iso":"eng"}],"oa_version":"Preprint","article_processing_charge":"No","quality_controlled":"1","article_type":"original","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","department":[{"_id":"RoSe"}],"arxiv":1,"date_published":"2023-02-21T00:00:00Z","acknowledgement":"We are grateful to Rupert Frank for helpful discussions at an early stage of this project.\r\nFunding from the European Union’s Horizon 2020 research and innovation programme\r\nunder the ERC grant agreement No 694227 is acknowledged."},{"ec_funded":1,"day":"21","_id":"15013","date_created":"2024-02-18T23:01:03Z","oa":1,"issue":"2","publication_status":"published","citation":{"ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>.","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>"},"external_id":{"arxiv":["1907.13631"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"05","doi":"10.2140/pmp.2021.2.221","author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"orcid":"0000-0002-4821-3297","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","last_name":"Krüger"}],"publication":"Probability and Mathematical Physics","corr_author":"1","year":"2021","publisher":"Mathematical Sciences Publishers","date_updated":"2025-04-15T08:05:02Z","title":"Spectral radius of random matrices with independent entries","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"article_type":"original","quality_controlled":"1","article_processing_charge":"No","oa_version":"Preprint","page":"221-280","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge."}],"status":"public","type":"journal_article","volume":2,"intvolume":"         2","acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","arxiv":1,"date_published":"2021-05-21T00:00:00Z","department":[{"_id":"LaEr"}],"scopus_import":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]}]