---
_id: '59213'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n          <jats:p>We compare a mean-field
    Gibbs distribution on a finite state space on <jats:italic>N</jats:italic> spins
    to that of an explicit simple mixture of product measures. This illustrates the
    situation beyond the so-called <jats:italic>increasing propagation of chaos</jats:italic>
    introduced by Ben Arous and Zeitouni [3], where marginal distributions of size
    <jats:inline-formula>\r\n              <jats:alternatives>\r\n                <jats:tex-math>$$k=o(N)$$</jats:tex-math>\r\n
    \               <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>k</mml:mi>\r\n                    <mml:mo>=</mml:mo>\r\n
    \                   <mml:mi>o</mml:mi>\r\n                    <mml:mo>(</mml:mo>\r\n
    \                   <mml:mi>N</mml:mi>\r\n                    <mml:mo>)</mml:mo>\r\n
    \                 </mml:mrow>\r\n                </mml:math>\r\n              </jats:alternatives>\r\n
    \           </jats:inline-formula> are compared to product measures.</jats:p>"
article_number: '6'
author:
- first_name: Jonas
  full_name: Jalowy, Jonas
  id: '113768'
  last_name: Jalowy
  orcid: 0000-0001-9624-2685
- first_name: Zakhar
  full_name: Kabluchko, Zakhar
  last_name: Kabluchko
- first_name: Matthias
  full_name: Löwe, Matthias
  last_name: Löwe
citation:
  ama: Jalowy J, Kabluchko Z, Löwe M. Propagation of Chaos and Residual Dependence
    in Gibbs Measures on Finite Sets. <i>Mathematical Physics, Analysis and Geometry</i>.
    2025;28(1). doi:<a href="https://doi.org/10.1007/s11040-025-09503-5">10.1007/s11040-025-09503-5</a>
  apa: Jalowy, J., Kabluchko, Z., &#38; Löwe, M. (2025). Propagation of Chaos and
    Residual Dependence in Gibbs Measures on Finite Sets. <i>Mathematical Physics,
    Analysis and Geometry</i>, <i>28</i>(1), Article 6. <a href="https://doi.org/10.1007/s11040-025-09503-5">https://doi.org/10.1007/s11040-025-09503-5</a>
  bibtex: '@article{Jalowy_Kabluchko_Löwe_2025, title={Propagation of Chaos and Residual
    Dependence in Gibbs Measures on Finite Sets}, volume={28}, DOI={<a href="https://doi.org/10.1007/s11040-025-09503-5">10.1007/s11040-025-09503-5</a>},
    number={16}, journal={Mathematical Physics, Analysis and Geometry}, publisher={Springer
    Science and Business Media LLC}, author={Jalowy, Jonas and Kabluchko, Zakhar and
    Löwe, Matthias}, year={2025} }'
  chicago: Jalowy, Jonas, Zakhar Kabluchko, and Matthias Löwe. “Propagation of Chaos
    and Residual Dependence in Gibbs Measures on Finite Sets.” <i>Mathematical Physics,
    Analysis and Geometry</i> 28, no. 1 (2025). <a href="https://doi.org/10.1007/s11040-025-09503-5">https://doi.org/10.1007/s11040-025-09503-5</a>.
  ieee: 'J. Jalowy, Z. Kabluchko, and M. Löwe, “Propagation of Chaos and Residual
    Dependence in Gibbs Measures on Finite Sets,” <i>Mathematical Physics, Analysis
    and Geometry</i>, vol. 28, no. 1, Art. no. 6, 2025, doi: <a href="https://doi.org/10.1007/s11040-025-09503-5">10.1007/s11040-025-09503-5</a>.'
  mla: Jalowy, Jonas, et al. “Propagation of Chaos and Residual Dependence in Gibbs
    Measures on Finite Sets.” <i>Mathematical Physics, Analysis and Geometry</i>,
    vol. 28, no. 1, 6, Springer Science and Business Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s11040-025-09503-5">10.1007/s11040-025-09503-5</a>.
  short: J. Jalowy, Z. Kabluchko, M. Löwe, Mathematical Physics, Analysis and Geometry
    28 (2025).
date_created: 2025-03-31T07:17:19Z
date_updated: 2025-04-23T14:39:12Z
doi: 10.1007/s11040-025-09503-5
intvolume: '        28'
issue: '1'
language:
- iso: eng
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
  issn:
  - 1385-0172
  - 1572-9656
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets
type: journal_article
user_id: '113768'
volume: 28
year: '2025'
...