[{"issue":"1","publication_identifier":{"issn":["1385-0172","1572-9656"]},"publication_status":"published","intvolume":"        28","citation":{"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>","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).","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} }","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>","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>.","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>."},"year":"2025","volume":28,"date_created":"2025-03-31T07:17:19Z","author":[{"first_name":"Jonas","id":"113768","full_name":"Jalowy, Jonas","last_name":"Jalowy","orcid":"0000-0001-9624-2685"},{"last_name":"Kabluchko","full_name":"Kabluchko, Zakhar","first_name":"Zakhar"},{"last_name":"Löwe","full_name":"Löwe, Matthias","first_name":"Matthias"}],"date_updated":"2025-04-23T14:39:12Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s11040-025-09503-5","title":"Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets","publication":"Mathematical Physics, Analysis and Geometry","type":"journal_article","status":"public","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>"}],"user_id":"113768","_id":"59213","language":[{"iso":"eng"}],"article_number":"6"}]