Propagation of chaos and residual dependence in Gibbs measures on finite sets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916431986163712 |
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| author | Jalowy, Jonas Kabluchko, Zakhar Löwe, Matthias |
| author_facet | Jalowy, Jonas Kabluchko, Zakhar Löwe, Matthias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Propagation of chaos and residual dependence in Gibbs measures on finite sets Jalowy, Jonas Kabluchko, Zakhar Löwe, Matthias Probability Mathematical Physics Primary: 82B05, Secondary: 82B20 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. |
| title | Propagation of chaos and residual dependence in Gibbs measures on finite sets |
| topic | Probability Mathematical Physics Primary: 82B05, Secondary: 82B20 |
| url | https://arxiv.org/abs/2410.08004 |