Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

A stochastic min-driven coalescence process and its hydrodynamical limit

Anne-Laure Basdevant, Philippe Laurençot, James R. Norris, and Clément Rau

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 47, Number 2 (2011), 329-357.

Dates
First available in Project Euclid: 23 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1300887272

Digital Object Identifier
doi:10.1214/09-AIHP349

Mathematical Reviews number (MathSciNet)
MR2814413

Zentralblatt MATH identifier
1216.82024

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60H10: Stochastic ordinary differential equations [See also 34F05] 34A34: Nonlinear equations and systems, general 34C11: Growth, boundedness

Keywords
Stochastic coalescence Min-driven clustering Hydrodynamical limit

Citation

Basdevant, Anne-Laure; Laurençot, Philippe; Norris, James R.; Rau, Clément. A stochastic min-driven coalescence process and its hydrodynamical limit. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 2, 329--357. doi:10.1214/09-AIHP349. https://projecteuclid.org/euclid.aihp/1300887272


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