### Abstract

Let μ^{(N)} denote a mean-field measure with potential F. Asymptotic independence properties of the measure μ^{(N)} are investigated. In particular, with H (·\μ) denoting relative entropy, if there exists a unique non-degenerate minimum of H (·\μ) - F(·), then propagation of chaos holds for blocks of size o(N). Certain degenerate situations are also studied. The results are applied for the Langevin dynamics of a system of interacting particles leading to a McKean-Vlasov limit.

Original language | English (US) |
---|---|

Pages (from-to) | 85-102 |

Number of pages | 18 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 35 |

Issue number | 1 |

State | Published - Jan 1999 |

### Fingerprint

### Keywords

- Exchangeability
- Gibbs potential
- Large deviations

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Annales de l'institut Henri Poincare (B) Probability and Statistics*,

*35*(1), 85-102.

**Increasing propagation of chaos for mean field models.** / Arous, G. Ben; Zeitouni, O.

Research output: Contribution to journal › Article

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 35, no. 1, pp. 85-102.

}

TY - JOUR

T1 - Increasing propagation of chaos for mean field models

AU - Arous, G. Ben

AU - Zeitouni, O.

PY - 1999/1

Y1 - 1999/1

N2 - Let μ(N) denote a mean-field measure with potential F. Asymptotic independence properties of the measure μ(N) are investigated. In particular, with H (·\μ) denoting relative entropy, if there exists a unique non-degenerate minimum of H (·\μ) - F(·), then propagation of chaos holds for blocks of size o(N). Certain degenerate situations are also studied. The results are applied for the Langevin dynamics of a system of interacting particles leading to a McKean-Vlasov limit.

AB - Let μ(N) denote a mean-field measure with potential F. Asymptotic independence properties of the measure μ(N) are investigated. In particular, with H (·\μ) denoting relative entropy, if there exists a unique non-degenerate minimum of H (·\μ) - F(·), then propagation of chaos holds for blocks of size o(N). Certain degenerate situations are also studied. The results are applied for the Langevin dynamics of a system of interacting particles leading to a McKean-Vlasov limit.

KW - Exchangeability

KW - Gibbs potential

KW - Large deviations

UR - http://www.scopus.com/inward/record.url?scp=0032615649&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032615649&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032615649

VL - 35

SP - 85

EP - 102

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 1

ER -