[{"scopus_import":"1","issue":"9","publication":"Calculus of Variations and Partial Differential Equations","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"acknowledgement":"The author would like to express his sincere gratitude to Nicolas Rougerie for introducing him to the problem, for his hospitality, and for the precious discussions. The author would also like to thank Douglas Lundholm and the anonymous referee for their precious feedback. Partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the TRR 352 Project ID 470903074 and by the European Research Council through the ERC CoG RAMBAS Project Nr. 101044249 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","OA_place":"publisher","OA_type":"hybrid","language":[{"iso":"eng"}],"status":"public","date_created":"2026-09-22T05:35:39Z","author":[{"full_name":"Visconti, Francois L","first_name":"Francois L","last_name":"Visconti","id":"8d897387-8b69-11f1-b3df-9a1e4632e81d"}],"title":"Average-field approximation for dilute almost-bosonic anyons","_id":"22970","extern":"1","abstract":[{"lang":"eng","text":"We study the ground state of a system of N two-dimensional trapped almost-bosonic anyons. This setup can equivalently be viewed as bosons interacting through long-range magnetic potentials generated by magnetic charges carried by each particle. These magnetic charges are assumed to be smeared over discs of radius R—a model known as extended anyons. To recover the point-like anyons perspective, we consider the joint limit R -> 0 as N →∞. We rigorously justify the average-field approximation for any radius R that decays polynomially, and even for certain exponentially decaying R. The average-field approximation asserts that the particles behave like independent, identical bosons interacting through a self-consistent magnetic field. Our result significantly improves upon the best-known estimates from [1, 2], and it in particular covers radii that are much smaller than the mean interparticle distance. The proof strategy builds on a recent work on two-dimensional attractive Bose gases by Junge and the author [3]."}],"oa_version":"Published Version","type":"journal_article","article_type":"original","citation":{"ama":"Visconti FL. Average-field approximation for dilute almost-bosonic anyons. <i>Calculus of Variations and Partial Differential Equations</i>. 2026;65(9). doi:<a href=\"https://doi.org/10.1007/s00526-026-03428-9\">10.1007/s00526-026-03428-9</a>","mla":"Visconti, Francois L. “Average-Field Approximation for Dilute Almost-Bosonic Anyons.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 9, 260, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s00526-026-03428-9\">10.1007/s00526-026-03428-9</a>.","ieee":"F. L. Visconti, “Average-field approximation for dilute almost-bosonic anyons,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 65, no. 9. Springer, 2026.","short":"F.L. Visconti, Calculus of Variations and Partial Differential Equations 65 (2026).","ista":"Visconti FL. 2026. Average-field approximation for dilute almost-bosonic anyons. Calculus of Variations and Partial Differential Equations. 65(9), 260.","chicago":"Visconti, Francois L. “Average-Field Approximation for Dilute Almost-Bosonic Anyons.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s00526-026-03428-9\">https://doi.org/10.1007/s00526-026-03428-9</a>.","apa":"Visconti, F. L. (2026). Average-field approximation for dilute almost-bosonic anyons. <i>Calculus of Variations and Partial Differential Equations</i>. Springer. <a href=\"https://doi.org/10.1007/s00526-026-03428-9\">https://doi.org/10.1007/s00526-026-03428-9</a>"},"DOAJ_listed":"1","license":"https://creativecommons.org/licenses/by/4.0/","PlanS_conform":"1","date_updated":"2026-10-20T14:10:55Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"dataavailabilitystatement":"Data sharing not applicable to this article as no datasets were generated or analysed during the current study.","day":"12","publisher":"Springer","month":"09","external_id":{"pmid":["42733399"]},"article_number":"260","doi":"10.1007/s00526-026-03428-9","file":[{"file_id":"23179","file_size":587149,"content_type":"application/pdf","date_updated":"2026-10-20T14:08:18Z","file_name":"2026_CalculusVariations_Visconti.pdf","date_created":"2026-10-20T14:08:18Z","checksum":"4599427a622cd93a96e3ca0465e0ccf5","success":1,"relation":"main_file","creator":"dernst","access_level":"open_access"}],"volume":65,"ddc":["500"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"intvolume":"        65","publication_status":"published","year":"2026","pmid":1,"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","date_published":"2026-09-12T00:00:00Z","file_date_updated":"2026-10-20T14:08:18Z","das_tickbox":"1","fulldoi":"https://doi.org/10.1007/s00526-026-03428-9"}]