---
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
fulldoi: https://doi.org/10.1214/25-aop1763
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'
...
---
OA_place: repository
OA_type: green
_id: '21271'
abstract:
- lang: eng
text: For general non-Hermitian large random matrices X and deterministic deformation
matrices A, we prove that the local eigenvalue statistics of A+X close to the
typical edge points of its spectrum are universal. Furthermore, we show that,
under natural assumptions, on A the spectrum of A+X does not have outliers at
a distance larger than the natural fluctuation scale of the eigenvalues. As a
consequence, the number of eigenvalues in each component of Spec(A+X) is deterministic.
acknowledgement: The authors would like to thank the anonymous referee for providing
helpful comments and suggestions. We also thank Joscha Henheik and Volodymyr Riabov
for pointing out a gap in an earlier version of the proof of equation (3.18). The
first, third, and fourth authors are supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andrew J
full_name: Campbell, Andrew J
id: 582b06a9-1f1c-11ee-b076-82ffce00dde4
last_name: Campbell
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Campbell AJ, Cipolloni G, Erdös L, Ji HC. On the spectral edge of non-Hermitian
random matrices. The Annals of Probability. 2025;53(6):2256-2308. doi:10.1214/25-aop1761
apa: Campbell, A. J., Cipolloni, G., Erdös, L., & Ji, H. C. (2025). On the spectral
edge of non-Hermitian random matrices. The Annals of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/25-aop1761
chicago: Campbell, Andrew J, Giorgio Cipolloni, László Erdös, and Hong Chang Ji.
“On the Spectral Edge of Non-Hermitian Random Matrices.” The Annals of Probability.
Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/25-aop1761.
ieee: A. J. Campbell, G. Cipolloni, L. Erdös, and H. C. Ji, “On the spectral edge
of non-Hermitian random matrices,” The Annals of Probability, vol. 53,
no. 6. Institute of Mathematical Statistics, pp. 2256–2308, 2025.
ista: Campbell AJ, Cipolloni G, Erdös L, Ji HC. 2025. On the spectral edge of non-Hermitian
random matrices. The Annals of Probability. 53(6), 2256–2308.
mla: Campbell, Andrew J., et al. “On the Spectral Edge of Non-Hermitian Random Matrices.”
The Annals of Probability, vol. 53, no. 6, Institute of Mathematical Statistics,
2025, pp. 2256–308, doi:10.1214/25-aop1761.
short: A.J. Campbell, G. Cipolloni, L. Erdös, H.C. Ji, The Annals of Probability
53 (2025) 2256–2308.
corr_author: '1'
date_created: 2026-02-17T07:58:20Z
date_published: 2025-11-01T00:00:00Z
date_updated: 2026-02-18T08:35:38Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/25-aop1761
ec_funded: 1
external_id:
arxiv:
- '2404.17512'
fulldoi: https://doi.org/10.1214/25-aop1761
intvolume: ' 53'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2404.17512
month: '11'
oa: 1
oa_version: Preprint
page: 2256-2308
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: On the spectral edge of non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2025'
...
---
_id: '11354'
abstract:
- lang: eng
text: We construct a recurrent diffusion process with values in the space of probability
measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process
is associated with the Dirichlet form defined by integration of the Wasserstein
gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional
base spaces to the modified massive Arratia flow over the unit interval described
in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800).
Together with two different constructions of the process, we discuss its ergodicity,
invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff
Center for Mathematics. The author gratefully acknowledges funding of his current
position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the
European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr.
Jan Maas).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648.
doi:10.1214/21-AOP1541
apa: Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of
probability measures over a closed Riemannian manifold. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541
chicago: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space
of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability.
Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.
ieee: L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold,” Annals of Probability, vol.
50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.
ista: Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.
mla: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability
Measures over a Closed Riemannian Manifold.” Annals of Probability, vol.
50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.
short: L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.
corr_author: '1'
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2025-04-14T07:27:47Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AOP1541
ec_funded: 1
external_id:
arxiv:
- '1811.11598'
isi:
- '000773518500005'
fulldoi: https://doi.org/10.1214/21-AOP1541
intvolume: ' 50'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1811.11598'
month: '03'
oa: 1
oa_version: Preprint
page: 591-648
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: 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: The Dirichlet–Ferguson diffusion on the space of probability measures over
a closed Riemannian manifold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2022'
...
---
_id: '11418'
abstract:
- lang: eng
text: "We consider the quadratic form of a general high-rank deterministic matrix
on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian
fluctuation for each bulk eigenvector in the large N limit. The proof is a combination
of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau
(2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021)
1005–1048)."
acknowledgement: L.E. would like to thank Zhigang Bao for many illuminating discussions
in an early stage of this research. The authors are also grateful to Paul Bourgade
for his comments on the manuscript and the anonymous referee for several useful
suggestions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity
for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation
in quantum ergodicity for Wigner matrices. Annals of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation
in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum
ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3.
Institute of Mathematical Statistics, pp. 984–1012, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity
for Wigner matrices. Annals of Probability. 50(3), 984–1012.
mla: Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner
Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical
Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.
date_created: 2022-05-29T22:01:53Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-03T07:16:53Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/21-AOP1552
external_id:
arxiv:
- '2103.06730'
isi:
- '000793963400005'
fulldoi: https://doi.org/10.1214/21-AOP1552
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.06730
month: '05'
oa: 1
oa_version: Preprint
page: 984-1012
publication: 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: Normal fluctuation in quantum ergodicity for Wigner matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 50
year: '2022'
...