---
_id: '15307'
article_processing_charge: No
author:
- first_name: Doris
  full_name: Ernst, Doris
  id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
  last_name: Ernst
  orcid: 0000-0002-2354-0195
citation:
  ama: Ernst D. Troll. <i>Trollhausen</i>. 2025.
  apa: Ernst, D. (2025). Troll. <i>Trollhausen</i>. Trollingten.
  chicago: Ernst, Doris. “Troll.” <i>Trollhausen</i>. Trollingten, 2025.
  ieee: D. Ernst, “Troll,” <i>Trollhausen</i>. Trollingten, 2025.
  ista: Ernst D. 2025. Troll. Trollhausen.
  mla: Ernst, Doris. “Troll.” <i>Trollhausen</i>, Trollingten, 2025.
  short: D. Ernst, Trollhausen (2025).
das_tickbox: '1'
date_created: 2025-08-12T10:21:09Z
date_published: 2025-08-12T00:00:00Z
date_updated: 2026-04-02T09:51:57Z
day: '12'
department:
- _id: E-Lib
external_id:
  chemrxivID:
  - 10.26434/chemrxiv.15001524
genbank:
- A45B12
- '12345'
keyword:
- Norway
- Troll
- Fjell
language:
- iso: eng
month: '08'
oa_version: None
publication: Trollhausen
publisher: Trollingten
status: public
title: Troll
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
_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
license: https://creativecommons.org/licenses/by/4.0/
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'
...