Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Propagation of chaos for a subcritical Keller–Segel model

David Godinho and Cristobal Quiñinao

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This paper deals with a subcritical Keller–Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical measure of the system tends towards the unique solution of the limit equation as the number of particles goes to infinity.


Cet article traite de l’équation de Keller–Segel dans un cadre sous-critique. À l’aide du système de particules en lien avec cette équation, nous montrons des résultats d’existence et d’unicité, puis la propagation du chaos pour ce dernier. Plus précisément, nous montrons que la mesure empirique du système tend vers l’unique solution de l’équation limite lorsque le nombre de particules tend vers l’infini.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 3 (2015), 965-992.

Received: 20 June 2013
Revised: 13 December 2013
Accepted: 23 January 2014
First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65C35: Stochastic particle methods [See also 82C80]

Keller–Segel Propagation of chaos Well-posedness


Godinho, David; Quiñinao, Cristobal. Propagation of chaos for a subcritical Keller–Segel model. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 3, 965--992. doi:10.1214/14-AIHP606.

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