---
res:
  bibo_abstract:
  - "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.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Federico
      foaf_name: Cornalba, Federico
      foaf_surname: Cornalba
  - foaf_Person:
      foaf_givenName: Julian L
      foaf_name: Fischer, Julian L
      foaf_surname: Fischer
      foaf_workInfoHomepage: http://www.librecat.org/personId=2C12A0B0-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-0479-558X
  - foaf_Person:
      foaf_givenName: Jonas
      foaf_name: Ingmanns, Jonas
      foaf_surname: Ingmanns
      foaf_workInfoHomepage: http://www.librecat.org/personId=71523d30-15b2-11ec-abd3-f80aa909d6b0
    orcid: 0009-0008-1310-7946
  - foaf_Person:
      foaf_givenName: Claudia
      foaf_name: Raithel, Claudia
      foaf_surname: Raithel
  bibo_doi: 10.1214/25-aop1763
  bibo_issue: '1'
  bibo_volume: 54
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0091-1798
  - http://id.crossref.org/issn/2168-894X
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_subject:
  - Weakly interacting particle systems
  - fluctuating hydrodynamics
  - Dean-Kawasaki equation
  - stochastic PDEs
  - numerical approximation
  dct_title: Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki
    equation@
...