no. 2
A stochastic min-driven coalescence process and its hydrodynamical limit
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 2, pp. 329-357.

L'évolution d'un système aléatoire de particules est étudiée lorsque la taille des particules croît par coagulation binaire, chaque réaction de coagulation impliquant nécessairement une particule de taille minimale. Nous montrons qu'une version renormalisée du processus stochastique associé converge vers une limite déterministe et étudions l'évolution temporelle de la taille minimale pour les modèles stochastique et déterministe.

A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalized version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.

DOI : 10.1214/09-AIHP349
Classification : 82C22, 60K35, 60H10, 34A34, 34C11
Mots clés : stochastic coalescence, min-driven clustering, hydrodynamical limit 
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     title = {A stochastic min-driven coalescence process and its hydrodynamical limit},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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Basdevant, Anne-Laure; Laurençot, Philippe; Norris, James R.; Rau, Clément. A stochastic min-driven coalescence process and its hydrodynamical limit. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 2, pp. 329-357. doi : 10.1214/09-AIHP349. http://www.numdam.org/articles/10.1214/09-AIHP349/

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