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

2024/10/10 by Jonas Jalowy, Jalowy, Jonas, Zakhar Kabluchko +3
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Primary: 82B05 #Probability (math.PR) #Secondary: 82B20

paper · pdf · doi:10.48550/arxiv.2410.08004

openalex publication_date 2024/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Decomposition of mean-field Gibbs distributions into product measures
• Size of chaos for Gibbs measures of mean field interacting diffusions
• When does the chaos in the Curie-Weiss model stop to propagate?
• Gibbs measures of disordered lattice systems with unbounded spins
• (Non-) Gibbsianness and phase transitions in random lattice spin models