---
_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. <i>Probability Theory and Related Fields</i>. 2024. doi:<a
    href="https://doi.org/10.1007/s00440-023-01254-0">10.1007/s00440-023-01254-0</a>
  apa: Clozeau, N., &#38; Mattesini, F. (2024). Annealed quantitative estimates for
    the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related
    Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-023-01254-0">https://doi.org/10.1007/s00440-023-01254-0</a>
  chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
    for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory
    and Related Fields</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00440-023-01254-0">https://doi.org/10.1007/s00440-023-01254-0</a>.
  ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic
    2D-discrete random matching problem,” <i>Probability Theory and Related Fields</i>.
    Springer Nature, 2024.
  ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic
    2D-discrete random matching problem. Probability Theory and Related Fields.
  mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
    for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory
    and Related Fields</i>, Springer Nature, 2024, doi:<a href="https://doi.org/10.1007/s00440-023-01254-0">10.1007/s00440-023-01254-0</a>.
  short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields (2024).
date_created: 2024-01-14T23:00:57Z
date_published: 2024-01-04T00:00:00Z
date_updated: 2025-08-12T12:22:41Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01254-0
ec_funded: 1
external_id:
  arxiv:
  - '2303.00353'
has_accepted_license: '1'
keyword:
- Troll
- Norway
- Fjell
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s00440-023-01254-0
month: '01'
oa: 1
oa_version: Published Version
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: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Annealed quantitative estimates for the quadratic 2D-discrete random matching
  problem
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: '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. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a
    href="https://doi.org/10.1007/s00440-022-01156-7">10.1007/s00440-022-01156-7</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality
    for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00440-022-01156-7">https://doi.org/10.1007/s00440-022-01156-7</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality
    for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer
    Nature, 2023. <a href="https://doi.org/10.1007/s00440-022-01156-7">https://doi.org/10.1007/s00440-022-01156-7</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed
    Wigner matrices,” <i>Probability Theory and Related Fields</i>, 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.”
    <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023,
    pp. 1183–1218, doi:<a href="https://doi.org/10.1007/s00440-022-01156-7">10.1007/s00440-022-01156-7</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
    185 (2023) 1183–1218.
date_created: 2022-08-07T22:02:00Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-14T12:48:09Z
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: '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 0<a<1/2. This extends our previous
    result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that
    was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime.
    The main novelty is a local law for the product of resolvents for the Hermitization
    of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic
    regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem
    of the characteristic flow method and the Green function comparison idea combined
    with a separation of the unstable mode of the underlying stability operator."
acknowledgement: The authors are grateful to Joscha Henheik for his help with the
  formulas in Appendix B.
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. Mesoscopic central limit theorem for non-Hermitian
    random matrices. <i>Probability Theory and Related Fields</i>. 2023. doi:<a href="https://doi.org/10.1007/s00440-023-01229-1">10.1007/s00440-023-01229-1</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Mesoscopic central
    limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related
    Fields</i>. Springer Nature. <a href="https://doi.org/10.1007/s00440-023-01229-1">https://doi.org/10.1007/s00440-023-01229-1</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central
    Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related
    Fields</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00440-023-01229-1">https://doi.org/10.1007/s00440-023-01229-1</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem
    for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>.
    Springer Nature, 2023.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem
    for non-Hermitian random matrices. Probability Theory and Related Fields.
  mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian
    Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature,
    2023, doi:<a href="https://doi.org/10.1007/s00440-023-01229-1">10.1007/s00440-023-01229-1</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
    (2023).
date_created: 2023-10-08T22:01:17Z
date_published: 2023-09-28T00:00:00Z
date_updated: 2023-10-09T07:19:01Z
day: '28'
department:
- _id: LaEr
doi: 10.1007/s00440-023-01229-1
external_id:
  arxiv:
  - '2210.12060'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2210.12060
month: '09'
oa: 1
oa_version: Preprint
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: Mesoscopic central limit theorem for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...