# Captivity of mean-field systems

Abstract : The aim of this work is to establish the stability of mean-field system under non-convex confining potential. A mean-field system corresponds to a system of $N$ particles in weak interaction and confined by an exterior force. With our hypotheses, it is a Kolmogorov diffusion with potential $\Upsilon^N$. Exit time of these systems have been studied in details in the small-noise limit. Here, we will deal with the large-dimension limit with fixed noise. In one hand, we show that the meta-potential $\Upsilon^N$ admits a number of wells which tends to infinity when $N$ goes to infinity. In the other hand, by using the convergence of McKean-Vlasov processes in long-time and the propagation of chaos, we prove that there exist traps such that the diffusion can not escape from. Furthermore, the traps do not coincide with the wells of $\Upsilon^N$.
Type de document :
Pré-publication, Document de travail
2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00573047
Contributeur : Julian Tugaut <>
Soumis le : vendredi 30 septembre 2011 - 16:37:57
Dernière modification le : vendredi 30 septembre 2011 - 17:32:16
Document(s) archivé(s) le : samedi 31 décembre 2011 - 02:40:40

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Captivity2.pdf
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### Identifiants

• HAL Id : hal-00573047, version 2

### Citation

Julian Tugaut. Captivity of mean-field systems. 2011. <hal-00573047v2>

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