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Propagation of chaos and residual dependence in Gibbs measures on finite sets

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arxiv 2410.08004 v1 pith:QN6ISFU3 submitted 2024-10-10 math.PR math-phmath.MP

Jonas Jalowy , Zakhar Kabluchko , Matthias Löwe This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords measureschaosfinitegibbsproductpropagationarousbeyond
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abstract

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 1999, where marginal distributions of size $k=o(N)$ are compared to product measures.

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