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<p>We compare a mean-field Gibbs distribution on a finite state space on <i>N</i> spins to that of an explicit simple mixture of product measures. This illustrates the situation beyond the so-called <i>increasing propagation of chaos</i> introduced by Ben Arous and Zeitouni [<CitationRef CitationID="CR3">3</CitationRef>], where marginal distributions of size <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11040_2025_9503_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=o(N)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mi>o</mi> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are compared to product measures.</p>

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Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月15日

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  • Jonas Jalowy,
  • Zakhar Kabluchko,
  • Matthias Löwe

摘要

We compare a mean-field Gibbs distribution on a finite state space on N spins to that of an explicit simple mixture of product measures. This illustrates the situation beyond the so-called increasing propagation of chaos introduced by Ben Arous and Zeitouni [3], where marginal distributions of size \(k=o(N)\) k = o ( N ) are compared to product measures.