Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets
J. Jalowy, Z. Kabluchko, M. Löwe, Mathematical Physics, Analysis and Geometry 28 (2025).
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Journal Article
| Published
| English
Author
Jalowy, Jonas;
Kabluchko, Zakhar;
Löwe, Matthias
Abstract
<jats:title>Abstract</jats:title>
<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>
<jats:alternatives>
<jats:tex-math>$$k=o(N)$$</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>o</mml:mi>
<mml:mo>(</mml:mo>
<mml:mi>N</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math>
</jats:alternatives>
</jats:inline-formula> are compared to product measures.</jats:p>
Publishing Year
Journal Title
Mathematical Physics, Analysis and Geometry
Volume
28
Issue
1
Article Number
6
LibreCat-ID
Cite this
Jalowy J, Kabluchko Z, Löwe M. Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets. Mathematical Physics, Analysis and Geometry. 2025;28(1). doi:10.1007/s11040-025-09503-5
Jalowy, J., Kabluchko, Z., & Löwe, M. (2025). Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets. Mathematical Physics, Analysis and Geometry, 28(1), Article 6. https://doi.org/10.1007/s11040-025-09503-5
@article{Jalowy_Kabluchko_Löwe_2025, title={Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets}, volume={28}, DOI={10.1007/s11040-025-09503-5}, 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} }
Jalowy, Jonas, Zakhar Kabluchko, and Matthias Löwe. “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets.” Mathematical Physics, Analysis and Geometry 28, no. 1 (2025). https://doi.org/10.1007/s11040-025-09503-5.
J. Jalowy, Z. Kabluchko, and M. Löwe, “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets,” Mathematical Physics, Analysis and Geometry, vol. 28, no. 1, Art. no. 6, 2025, doi: 10.1007/s11040-025-09503-5.
Jalowy, Jonas, et al. “Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets.” Mathematical Physics, Analysis and Geometry, vol. 28, no. 1, 6, Springer Science and Business Media LLC, 2025, doi:10.1007/s11040-025-09503-5.
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