---
OA_place: publisher
OA_type: hybrid
_id: '21379'
abstract:
- lang: eng
text: We study a (1 + 1)-dimensional semi-discrete random variational problem that
can be interpreted as the geometrically linearized version of the critical 2-dimensional
random field Ising model. The scaling of the correlation length of the latter
was recently characterized in Probab. Duke Math. J. 172(9), 1781–1811 (2023) and
arXiv:2011.08768v3, (2022); our analysis is reminiscent of the multi-scale approach
of the latter work and of Combinatorica 9, 161–187 (1989) . We show that at every
dyadic scale from the system size down to the lattice spacing the minimizer contains
at most order-one Dirichlet energy per unit length. We also establish a quenched
homogenization result in the sense that the leading order of the minimal energy
becomes deterministic as the ratio system size / lattice spacing diverges. To
this purpose we adapt arguments from arXiv:2401.06768, (2024) on the (d + 1)-dimensional
version our the model, with a Brownian replacing the white noise potential, to
obtain the initial large-scale bounds. Based on our estimate of the (p = 3)-Dirichlet
energy, we give an informal justification of the geometric linearization. Our
bounds, which are oblivious to the microscopic cut-off scale provided by the lattice
spacing, yield tightness of the law of minimizers in the space of continuous functions
as the lattice spacing is sent to zero.
acknowledgement: FO and CW thank Ron Peled for insightful discussions on the white-noise
multi-dimensional case in the Fall of 2023. CW thanks Barbara Dembin for the discussion
during a workshop in Spring 2025. The work was done while the authors were affiliated
with the Max Planck Institute for Mathematics in the Sciences; CW thanks the MPI
for the support and warm hospitality. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Felix
full_name: Otto, Felix
last_name: Otto
- first_name: Matteo
full_name: Palmieri, Matteo
last_name: Palmieri
- first_name: Christian
full_name: Wagner, Christian
id: bf0c729b-2619-11f0-8024-9d69bb2b8b20
last_name: Wagner
citation:
ama: Otto F, Palmieri M, Wagner C. On minimizing curves in a Brownian potential.
Probability Theory and Related Fields. 2026. doi:10.1007/s00440-026-01468-y
apa: Otto, F., Palmieri, M., & Wagner, C. (2026). On minimizing curves in a
Brownian potential. Probability Theory and Related Fields. Springer Nature.
https://doi.org/10.1007/s00440-026-01468-y
chicago: Otto, Felix, Matteo Palmieri, and Christian Wagner. “On Minimizing Curves
in a Brownian Potential.” Probability Theory and Related Fields. Springer
Nature, 2026. https://doi.org/10.1007/s00440-026-01468-y.
ieee: F. Otto, M. Palmieri, and C. Wagner, “On minimizing curves in a Brownian potential,”
Probability Theory and Related Fields. Springer Nature, 2026.
ista: Otto F, Palmieri M, Wagner C. 2026. On minimizing curves in a Brownian potential.
Probability Theory and Related Fields.
mla: Otto, Felix, et al. “On Minimizing Curves in a Brownian Potential.” Probability
Theory and Related Fields, Springer Nature, 2026, doi:10.1007/s00440-026-01468-y.
short: F. Otto, M. Palmieri, C. Wagner, Probability Theory and Related Fields (2026).
corr_author: '1'
date_created: 2026-03-02T10:05:23Z
date_published: 2026-02-14T00:00:00Z
date_updated: 2026-03-02T15:15:13Z
day: '14'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-026-01468-y
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00440-026-01468-y
month: '02'
oa: 1
oa_version: Published Version
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On minimizing curves in a Brownian potential
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
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '19598'
abstract:
- lang: eng
text: We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue
statistics in the vicinity of the cusp-like singularities of the limiting spectral
density for Wigner-type random matrices. Prior to this work, the linear eigenvalue
statistics at the cusp-like singularities were not studied in any ensemble. Our
analysis covers not only the exact cusps but the entire transitionary regime from
the square-root singularity at a regular edge through the sharp cusp to the bulk.
We identify a new one-parameter family of functionals that govern the limiting
bias and variance, continuously interpolating between the previously known formulas
in the bulk and at a regular edge. Since cusps are the only possible singularities
besides the regular edges, our result gives a complete description of the linear
eigenvalue statistics in all regimes.
acknowledgement: I would like to express my gratitude to László Erdős for his careful
guidance and supervision of my work. I am also thankful to Jana Reker and Joscha
Henheik for many helpful discussions. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
citation:
ama: Riabov V. Linear Eigenvalue statistics at the cusp. Probability Theory and
Related Fields. 2025;193:1183-1237. doi:10.1007/s00440-025-01373-w
apa: Riabov, V. (2025). Linear Eigenvalue statistics at the cusp. Probability
Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01373-w
chicago: Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability
Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01373-w.
ieee: V. Riabov, “Linear Eigenvalue statistics at the cusp,” Probability Theory
and Related Fields, vol. 193. Springer Nature, pp. 1183–1237, 2025.
ista: Riabov V. 2025. Linear Eigenvalue statistics at the cusp. Probability Theory
and Related Fields. 193, 1183–1237.
mla: Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” Probability
Theory and Related Fields, vol. 193, Springer Nature, 2025, pp. 1183–237,
doi:10.1007/s00440-025-01373-w.
short: V. Riabov, Probability Theory and Related Fields 193 (2025) 1183–1237.
corr_author: '1'
date_created: 2025-04-20T22:01:28Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-04-07T12:32:19Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-025-01373-w
external_id:
arxiv:
- '2307.07432'
isi:
- '001466997300001'
file:
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checksum: 700229b280725c0d6aad0d71362cce5f
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creator: dernst
date_created: 2025-12-30T13:10:05Z
date_updated: 2025-12-30T13:10:05Z
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month: '12'
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oa_version: Published Version
page: 1183-1237
publication: Probability Theory and Related Fields
publication_identifier:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Linear Eigenvalue statistics at the cusp
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: 193
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19737'
abstract:
- lang: eng
text: For general large non–Hermitian random matrices X and deterministic normal
deformations A, we prove that the local eigenvalue statistics of A + X close to
the critical edge points of its spectrum are universal. This concludes the proof
of the third and last remaining typical universality class for non–Hermitian random
matrices (for normal deformations), after bulk and sharp edge universalities have
been established in recent years.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
article_number: '050603'
article_processing_charge: Yes (via OA deal)
article_type: original
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: Hong Chang
full_name: Ji, Hong Chang
last_name: Ji
citation:
ama: Cipolloni G, Erdös L, Ji HC. Non–Hermitian spectral universality at critical
points. Probability Theory and Related Fields. 2025. doi:10.1007/s00440-025-01384-7
apa: Cipolloni, G., Erdös, L., & Ji, H. C. (2025). Non–Hermitian spectral universality
at critical points. Probability Theory and Related Fields. Springer Nature.
https://doi.org/10.1007/s00440-025-01384-7
chicago: Cipolloni, Giorgio, László Erdös, and Hong Chang Ji. “Non–Hermitian Spectral
Universality at Critical Points.” Probability Theory and Related Fields.
Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01384-7.
ieee: G. Cipolloni, L. Erdös, and H. C. Ji, “Non–Hermitian spectral universality
at critical points,” Probability Theory and Related Fields. Springer Nature,
2025.
ista: Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at
critical points. Probability Theory and Related Fields., 050603.
mla: Cipolloni, Giorgio, et al. “Non–Hermitian Spectral Universality at Critical
Points.” Probability Theory and Related Fields, 050603, Springer Nature,
2025, doi:10.1007/s00440-025-01384-7.
short: G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025).
corr_author: '1'
date_created: 2025-05-25T22:16:59Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2026-06-18T18:17:57Z
day: '01'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1007/s00440-025-01384-7
ec_funded: 1
external_id:
isi:
- '001493091900001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00440-025-01384-7
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Non–Hermitian spectral universality at critical points
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20478'
abstract:
- lang: eng
text: 'We consider the Wigner minor process, i.e. the eigenvalues of an N\times
N Wigner matrix H^{(N)} together with the eigenvalues of all its n\times n minors,
H^{(n)}, n\le N. The top eigenvalues of H^{(N)} and those of its immediate minor
H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for
smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical
transition regime around k\sim N^{2/3} was analyzed by Forrester and Nagao (J.
Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the
nontrivial joint correlation function. We prove that this formula is universal,
i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis
of the sub- and supercritical regimes both for eigenvalues and for the corresponding
eigenvector overlaps, thus we prove the decorrelation transition in full generality.'
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121
and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by
the ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- 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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
orcid: 0000-0003-1491-4623
citation:
ama: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition
in the Wigner minor process. Probability Theory and Related Fields. 2025.
doi:10.1007/s00440-025-01422-4
apa: Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025).
Decorrelation transition in the Wigner minor process. Probability Theory and
Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01422-4
chicago: Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and
Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” Probability
Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01422-4.
ieee: Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation
transition in the Wigner minor process,” Probability Theory and Related Fields.
Springer Nature, 2025.
ista: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation
transition in the Wigner minor process. Probability Theory and Related Fields.
mla: Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.”
Probability Theory and Related Fields, Springer Nature, 2025, doi:10.1007/s00440-025-01422-4.
short: Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory
and Related Fields (2025).
corr_author: '1'
date_created: 2025-10-16T13:10:26Z
date_published: 2025-09-20T00:00:00Z
date_updated: 2026-06-18T18:23:40Z
day: '20'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1007/s00440-025-01422-4
ec_funded: 1
external_id:
arxiv:
- '2503.06549'
isi:
- '001574640900001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00440-025-01422-4
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decorrelation transition in the Wigner minor process
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
_id: '12485'
abstract:
- lang: eng
text: In this paper we introduce the critical variational setting for parabolic
stochastic evolution equations of quasi- or semi-linear type. Our results improve
many of the abstract results in the classical variational setting. In particular,
we are able to replace the usual weak or local monotonicity condition by a more
flexible local Lipschitz condition. Moreover, the usual growth conditions on the
multiplicative noise are weakened considerably. Our new setting provides general
conditions under which local and global existence and uniqueness hold. Moreover,
we prove continuous dependence on the initial data. We show that many classical
SPDEs, which could not be covered by the classical variational setting, do fit
in the critical variational setting. In particular, this is the case for the Cahn-Hilliard
equations, tamed Navier-Stokes equations, and Allen-Cahn equation.
acknowledgement: The first author has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819) . The second author is supported by the VICI subsidy
VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. The critical variational setting for stochastic evolution
equations. Probability Theory and Related Fields. 2024;188:957-1015. doi:10.1007/s00440-023-01249-x
apa: Agresti, A., & Veraar, M. (2024). The critical variational setting for
stochastic evolution equations. Probability Theory and Related Fields.
Springer Nature. https://doi.org/10.1007/s00440-023-01249-x
chicago: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for
Stochastic Evolution Equations.” Probability Theory and Related Fields.
Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01249-x.
ieee: A. Agresti and M. Veraar, “The critical variational setting for stochastic
evolution equations,” Probability Theory and Related Fields, vol. 188.
Springer Nature, pp. 957–1015, 2024.
ista: Agresti A, Veraar M. 2024. The critical variational setting for stochastic
evolution equations. Probability Theory and Related Fields. 188, 957–1015.
mla: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic
Evolution Equations.” Probability Theory and Related Fields, vol. 188,
Springer Nature, 2024, pp. 957–1015, doi:10.1007/s00440-023-01249-x.
short: A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.
date_created: 2023-02-02T10:45:15Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-04T11:27:46Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01249-x
ec_funded: 1
external_id:
arxiv:
- '2206.00230'
isi:
- '001154226500001'
file:
- access_level: open_access
checksum: b8572339dbc5b8de4934dc5fd34afc7d
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:21:09Z
date_updated: 2024-07-22T09:21:09Z
file_id: '17296'
file_name: 2024_ProbTheory_Agresti.pdf
file_size: 942801
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success: 1
file_date_updated: 2024-07-22T09:21:09Z
has_accepted_license: '1'
intvolume: ' 188'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 957-1015
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The critical variational setting for stochastic evolution equations
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 188
year: '2024'
...
---
_id: '14408'
abstract:
- lang: eng
text: "We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues
{σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries
are asymptotically Gaussian for any H20-functions f around any point z0 in the
bulk of the spectrum on any mesoscopic scale 0Probability Theory and Related Fields. 2024;188:1131-1182.
doi:10.1007/s00440-023-01229-1
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2024). Mesoscopic central
limit theorem for non-Hermitian random matrices. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central
Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related
Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01229-1.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem
for non-Hermitian random matrices,” Probability Theory and Related Fields,
vol. 188. Springer Nature, pp. 1131–1182, 2024.
ista: Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem
for non-Hermitian random matrices. Probability Theory and Related Fields. 188,
1131–1182.
mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian
Random Matrices.” Probability Theory and Related Fields, vol. 188, Springer
Nature, 2024, pp. 1131–82, doi:10.1007/s00440-023-01229-1.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
188 (2024) 1131–1182.
date_created: 2023-10-08T22:01:17Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-08-05T13:28:15Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00440-023-01229-1
ec_funded: 1
external_id:
arxiv:
- '2210.12060'
isi:
- '001118972500001'
intvolume: ' 188'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.12060
month: '04'
oa: 1
oa_version: Preprint
page: 1131-1182
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mesoscopic central limit theorem for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 188
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14797'
abstract:
- lang: eng
text: We study a random matching problem on closed compact 2 -dimensional Riemannian
manifolds (with respect to the squared Riemannian distance), with samples of random
points whose common law is absolutely continuous with respect to the volume measure
with strictly positive and bounded density. We show that given two sequences of
numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity,
the optimal transport plan between the two empirical measures μn and νm is
quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear
elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère
equation. This is obtained in the case of samples of correlated random points
for which a stretched exponential decay of the α -mixing coefficient holds and
for a class of discrete-time Markov chains having a unique absolutely continuous
invariant measure with respect to the volume measure.
acknowledgement: "NC has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (Grant
agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems.
FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics
Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute
for Mathematics in the Sciences."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Francesco
full_name: Mattesini, Francesco
last_name: Mattesini
citation:
ama: Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete
random matching problem. Probability Theory and Related Fields. 2024;190:485-541.
doi:10.1007/s00440-023-01254-0
apa: Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for
the quadratic 2D-discrete random matching problem. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0
chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.
ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic
2D-discrete random matching problem,” Probability Theory and Related Fields,
vol. 190. Springer Nature, pp. 485–541, 2024.
ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic
2D-discrete random matching problem. Probability Theory and Related Fields. 190,
485–541.
mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields, vol. 190, Springer Nature, 2024, pp. 485–541, doi:10.1007/s00440-023-01254-0.
short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024)
485–541.
corr_author: '1'
date_created: 2024-01-14T23:00:57Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:43:43Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01254-0
ec_funded: 1
external_id:
arxiv:
- '2303.00353'
isi:
- '001136206200002'
file:
- access_level: open_access
checksum: 34f44cad6a210ff66791ee37e590af2c
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:10:54Z
date_updated: 2025-01-09T08:10:54Z
file_id: '18788'
file_name: 2024_ProbTheoryRelatFields_Clozeau.pdf
file_size: 880117
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success: 1
file_date_updated: 2025-01-09T08:10:54Z
has_accepted_license: '1'
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language:
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month: '10'
oa: 1
oa_version: Published Version
page: 485-541
project:
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call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Annealed quantitative estimates for the quadratic 2D-discrete random matching
problem
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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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 190
year: '2024'
...
---
_id: '11741'
abstract:
- lang: eng
text: Following E. Wigner’s original vision, we prove that sampling the eigenvalue
gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the
celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly,
we prove universality for a monoparametric family of deformed Wigner matrices
H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just
using the randomness of a single scalar real random variable x. Both results constitute
quenched versions of bulk universality that has so far only been proven in annealed
sense with respect to the probability space of the matrix ensemble.
acknowledgement: "The authors are indebted to Sourav Chatterjee for forwarding the
very inspiring question that Stephen Shenker originally addressed to him which initiated
the current paper. They are also grateful that the authors of [23] kindly shared
their preliminary numerical results in June 2021.\r\nOpen access funding provided
by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
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. Quenched universality for deformed Wigner
matrices. Probability Theory and Related Fields. 2023;185:1183–1218. doi:10.1007/s00440-022-01156-7
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Quenched universality
for deformed Wigner matrices. Probability Theory and Related Fields. Springer
Nature. https://doi.org/10.1007/s00440-022-01156-7
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality
for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer
Nature, 2023. https://doi.org/10.1007/s00440-022-01156-7.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed
Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer
Nature, pp. 1183–1218, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed
Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.
mla: Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.”
Probability Theory and Related Fields, vol. 185, Springer Nature, 2023,
pp. 1183–1218, doi:10.1007/s00440-022-01156-7.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
185 (2023) 1183–1218.
corr_author: '1'
date_created: 2022-08-07T22:02:00Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2024-10-09T21:03:02Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-022-01156-7
external_id:
arxiv:
- '2106.10200'
isi:
- '000830344500001'
file:
- access_level: open_access
checksum: b9247827dae5544d1d19c37abe547abc
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T12:47:32Z
date_updated: 2023-08-14T12:47:32Z
file_id: '14054'
file_name: 2023_ProbabilityTheory_Cipolloni.pdf
file_size: 782278
relation: main_file
success: 1
file_date_updated: 2023-08-14T12:47:32Z
has_accepted_license: '1'
intvolume: ' 185'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1183–1218
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quenched universality for deformed Wigner matrices
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: 185
year: '2023'
...
---
_id: '8601'
abstract:
- lang: eng
text: We consider large non-Hermitian real or complex random matrices X with independent,
identically distributed centred entries. We prove that their local eigenvalue
statistics near the spectral edge, the unit circle, coincide with those of the
Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result
is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution
at the spectral edges of the Wigner ensemble.
article_processing_charge: Yes (via OA deal)
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. Edge universality for non-Hermitian random
matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for
non-Hermitian random matrices. Probability Theory and Related Fields. Springer
Nature. https://doi.org/10.1007/s00440-020-01003-7
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality
for Non-Hermitian Random Matrices.” Probability Theory and Related Fields.
Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian
random matrices,” Probability Theory and Related Fields. Springer Nature,
2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian
random matrices. Probability Theory and Related Fields.
mla: Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.”
Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
(2021).
corr_author: '1'
date_created: 2020-10-04T22:01:37Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-02T14:03:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-020-01003-7
ec_funded: 1
external_id:
arxiv:
- '1908.00969'
isi:
- '000572724600002'
file:
- access_level: open_access
checksum: 611ae28d6055e1e298d53a57beb05ef4
content_type: application/pdf
creator: dernst
date_created: 2020-10-05T14:53:40Z
date_updated: 2020-10-05T14:53:40Z
file_id: '8612'
file_name: 2020_ProbTheory_Cipolloni.pdf
file_size: 497032
relation: main_file
success: 1
file_date_updated: 2020-10-05T14:53:40Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Edge universality for non-Hermitian random matrices
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '319'
abstract:
- lang: eng
text: We study spaces of modelled distributions with singular behaviour near the
boundary of a domain that, in the context of the theory of regularity structures,
allow one to give robust solution theories for singular stochastic PDEs with boundary
conditions. The calculus of modelled distributions established in Hairer (Invent
Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended
to this setting. We formulate and solve fixed point problems in these spaces with
a class of kernels that is sufficiently large to cover in particular the Dirichlet
and Neumann heat kernels. These results are then used to provide solution theories
for the KPZ equation with Dirichlet and Neumann boundary conditions and for the
2D generalised parabolic Anderson model with Dirichlet boundary conditions. In
the case of the KPZ equation with Neumann boundary conditions, we show that, depending
on the class of mollifiers one considers, a “boundary renormalisation” takes place.
In other words, there are situations in which a certain boundary condition is
applied to an approximation to the KPZ equation, but the limiting process is the
Hopf–Cole solution to the KPZ equation with a different boundary condition.
acknowledgement: "MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Mate
full_name: Gerencser, Mate
id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
last_name: Gerencser
- first_name: Martin
full_name: Hairer, Martin
last_name: Hairer
citation:
ama: Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. Probability
Theory and Related Fields. 2019;173(3-4):697–758. doi:10.1007/s00440-018-0841-1
apa: Gerencser, M., & Hairer, M. (2019). Singular SPDEs in domains with boundaries.
Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0841-1
chicago: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0841-1.
ieee: M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” Probability
Theory and Related Fields, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.
ista: Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability
Theory and Related Fields. 173(3–4), 697–758.
mla: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
Probability Theory and Related Fields, vol. 173, no. 3–4, Springer, 2019,
pp. 697–758, doi:10.1007/s00440-018-0841-1.
short: M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019)
697–758.
corr_author: '1'
date_created: 2018-12-11T11:45:48Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2026-04-03T09:45:34Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00440-018-0841-1
external_id:
isi:
- '000463613800001'
file:
- access_level: open_access
checksum: 288d16ef7291242f485a9660979486e3
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:25:24Z
date_updated: 2020-07-14T12:46:03Z
file_id: '5722'
file_name: 2018_ProbTheory_Gerencser.pdf
file_size: 893182
relation: main_file
file_date_updated: 2020-07-14T12:46:03Z
has_accepted_license: '1'
intvolume: ' 173'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 697–758
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer
publist_id: '7546'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Singular SPDEs in domains with boundaries
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 173
year: '2019'
...
---
_id: '429'
abstract:
- lang: eng
text: We consider real symmetric or complex hermitian random matrices with correlated
entries. We prove local laws for the resolvent and universality of the local eigenvalue
statistics in the bulk of the spectrum. The correlations have fast decay but are
otherwise of general form. The key novelty is the detailed stability analysis
of the corresponding matrix valued Dyson equation whose solution is the deterministic
limit of the resolvent.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random
matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373.
doi:10.1007/s00440-018-0835-z
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix
Dyson equation and random matrices with correlations. Probability Theory and
Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the
Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory
and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation
and random matrices with correlations,” Probability Theory and Related Fields,
vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
ista: Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation
and random matrices with correlations. Probability Theory and Related Fields.
173(1–2), 293–373.
mla: Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random
Matrices with Correlations.” Probability Theory and Related Fields, vol.
173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
173 (2019) 293–373.
corr_author: '1'
date_created: 2018-12-11T11:46:25Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2026-04-03T09:46:51Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-018-0835-z
ec_funded: 1
external_id:
isi:
- '000459396500007'
file:
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checksum: f9354fa5c71f9edd17132588f0dc7d01
content_type: application/pdf
creator: dernst
date_created: 2018-12-17T16:12:08Z
date_updated: 2020-07-14T12:46:26Z
file_id: '5720'
file_name: 2018_ProbTheory_Ajanki.pdf
file_size: 1201840
relation: main_file
file_date_updated: 2020-07-14T12:46:26Z
has_accepted_license: '1'
intvolume: ' 173'
isi: 1
issue: 1-2
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 293–373
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer
publist_id: '7394'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stability of the matrix Dyson equation and random matrices with correlations
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 173
year: '2019'
...