Increasing propagation of chaos for mean field models

G. Ben Arous; O. Zeitouni

doi:10.1016/s0246-0203(99)80006-5

Increasing propagation of chaos for mean field models

G. Ben Arous, O. Zeitouni

Mathematics

Research output: Contribution to journal › Article › peer-review

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
DOIs	https://doi.org/10.1016/s0246-0203(99)80006-5
State	Published - 1999

Keywords

Exchangeability
Gibbs potential
Large deviations

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/s0246-0203(99)80006-5

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title = "Increasing propagation of chaos for mean field models",

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.",

keywords = "Exchangeability, Gibbs potential, Large deviations",

author = "Arous, {G. Ben} and O. Zeitouni",

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AU - Arous, G. Ben

AU - Zeitouni, O.

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PY - 1999

Y1 - 1999

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

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Increasing propagation of chaos for mean field models

Abstract

Keywords

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