---
APC_amount: 1352,08 EUR
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21894'
abstract:
- lang: eng
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."
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.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
last_name: Cornalba
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
orcid: 0009-0008-1310-7946
- first_name: Claudia
full_name: Raithel, Claudia
last_name: Raithel
citation:
ama: Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly
interacting particle systems via the Dean–Kawasaki equation. The Annals of
Probability. 2026;54(1):155-215. doi:10.1214/25-aop1763
apa: Cornalba, F., Fischer, J. L., Ingmanns, J., & Raithel, C. (2026). Density
fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation.
The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1763
chicago: Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel.
“Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki
Equation.” The Annals of Probability. Institute of Mathematical Statistics,
2026. https://doi.org/10.1214/25-aop1763.
ieee: F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations
in weakly interacting particle systems via the Dean–Kawasaki equation,” The
Annals of Probability, vol. 54, no. 1. Institute of Mathematical Statistics,
pp. 155–215, 2026.
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.
mla: Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle
Systems via the Dean–Kawasaki Equation.” The Annals of Probability, vol.
54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:10.1214/25-aop1763.
short: F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability
54 (2026) 155–215.
corr_author: '1'
date_created: 2026-05-20T08:25:25Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-05-21T07:21:25Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1214/25-aop1763
ec_funded: 1
external_id:
arxiv:
- '2303.00429'
file:
- access_level: open_access
checksum: 3e60c0e25a1c96342029a7d2b031505f
content_type: application/pdf
creator: dernst
date_created: 2026-05-21T07:11:27Z
date_updated: 2026-05-21T07:11:27Z
file_id: '21906'
file_name: 2026_AnnalsProbability_Cornalba.pdf
file_size: 865745
relation: main_file
success: 1
file_date_updated: 2026-05-21T07:11:27Z
has_accepted_license: '1'
intvolume: ' 54'
issue: '1'
keyword:
- Weakly interacting particle systems
- fluctuating hydrodynamics
- Dean-Kawasaki equation
- stochastic PDEs
- numerical approximation
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 155-215
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: The Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki
equation
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)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 54
year: '2026'
...