@article{59213,
  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>}},
  author       = {{Jalowy, Jonas and Kabluchko, Zakhar and Löwe, Matthias}},
  issn         = {{1385-0172}},
  journal      = {{Mathematical Physics, Analysis and Geometry}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets}}},
  doi          = {{10.1007/s11040-025-09503-5}},
  volume       = {{28}},
  year         = {{2025}},
}