[{"intvolume":"        54","publication_status":"published","year":"2026","file_date_updated":"2026-05-21T07:11:27Z","corr_author":"1","OA_type":"hybrid","PlanS_conform":"1","publication":"The Annals of Probability","scopus_import":"1","file":[{"date_created":"2026-05-21T07:11:27Z","date_updated":"2026-05-21T07:11:27Z","file_name":"2026_AnnalsProbability_Cornalba.pdf","creator":"dernst","file_id":"21906","access_level":"open_access","file_size":865745,"success":1,"checksum":"3e60c0e25a1c96342029a7d2b031505f","content_type":"application/pdf","relation":"main_file"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"arxiv":["2303.00429"]},"publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"ec_funded":1,"day":"01","author":[{"full_name":"Cornalba, Federico","last_name":"Cornalba","first_name":"Federico"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","first_name":"Julian L"},{"id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","full_name":"Ingmanns, Jonas","first_name":"Jonas","orcid":"0009-0008-1310-7946","last_name":"Ingmanns"},{"full_name":"Raithel, Claudia","last_name":"Raithel","first_name":"Claudia"}],"date_created":"2026-05-20T08:25:25Z","volume":54,"date_updated":"2026-05-21T07:21:25Z","doi":"10.1214/25-aop1763","_id":"21894","status":"public","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"keyword":["Weakly interacting particle systems","fluctuating hydrodynamics","Dean-Kawasaki equation","stochastic PDEs","numerical approximation"],"article_type":"original","oa_version":"Published Version","acknowledgement":"All authors gratefully acknowledge funding from the Austrian Science Fund (FWF) through the project F65. CR gratefully acknowledges support from the Austrian Science Fund (FWF), grants P30000, P33010, W1245. FC gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","issue":"1","APC_amount":"1352,08 EUR","page":"155-215","month":"01","department":[{"_id":"JuFi"}],"quality_controlled":"1","date_published":"2026-01-01T00:00:00Z","has_accepted_license":"1","abstract":[{"text":"The Dean–Kawasaki equation—one of the most fundamental SPDEs of\r\nfluctuating hydrodynamics—has been proposed as a model for density fluctuations in weakly interacting particle systems. In its original form, it is highly\r\nsingular and fails to be renormalizable, even by approaches such as regularity structures and paracontrolled distributions, hindering mathematical approaches to its rigorous justification. It has been understood recently that it is\r\nnatural to introduce a suitable regularization, for example, by applying a formal spatial discretization or by truncating high-frequency noise: This yields\r\nwell-posed equations that should still precisely approximate the law of the\r\nparticle density fluctuations.\r\nIn the present work, we prove that a regularization in the form of a formal\r\ndiscretization of the Dean–Kawasaki equation indeed accurately describes\r\ndensity fluctuations in systems of weakly interacting diffusing particles: We\r\nshow that, in suitable weak metrics, the law of fluctuations as predicted by\r\nthe discretized Dean–Kawasaki SPDE approximates the law of fluctuations\r\nof the original particle system, up to an error that is of arbitrarily high order in\r\nthe inverse particle number and a discretization error. In particular, the Dean–\r\nKawasaki equation provides a means for efficient and accurate simulations of\r\ndensity fluctuations in weakly interacting particle systems.","lang":"eng"}],"publisher":"Institute of Mathematical Statistics","OA_place":"publisher","citation":{"ista":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. 2026. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals of Probability. 54(1), 155–215.","ama":"Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. <i>The Annals of Probability</i>. 2026;54(1):155-215. doi:<a href=\"https://doi.org/10.1214/25-aop1763\">10.1214/25-aop1763</a>","chicago":"Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2026. <a href=\"https://doi.org/10.1214/25-aop1763\">https://doi.org/10.1214/25-aop1763</a>.","mla":"Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki Equation.” <i>The Annals of Probability</i>, vol. 54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:<a href=\"https://doi.org/10.1214/25-aop1763\">10.1214/25-aop1763</a>.","short":"F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability 54 (2026) 155–215.","ieee":"F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation,” <i>The Annals of Probability</i>, vol. 54, no. 1. Institute of Mathematical Statistics, pp. 155–215, 2026.","apa":"Cornalba, F., Fischer, J. L., Ingmanns, J., &#38; Raithel, C. (2026). Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aop1763\">https://doi.org/10.1214/25-aop1763</a>"},"arxiv":1,"type":"journal_article","title":"Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation"}]