The Annals of Applied Probability

Brownian coagulation and a version of Smoluchowski’s equation on the circle

Inés Armendáriz

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Abstract

We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion coefficients, the coagulation rates and the initial distribution of particles, we derive a spatially inhomogeneous version of the mass flow equation as the particle number tends to infinity. The mass flow equation is in one-to-one correspondence with Smoluchowski’s coagulation equation. We prove uniqueness for this equation in a broad class of solutions, to which the weak limit of the stochastic system is shown to belong.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 2 (2010), 660-695.

Dates
First available in Project Euclid: 9 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1268143436

Digital Object Identifier
doi:10.1214/09-AAP633

Mathematical Reviews number (MathSciNet)
MR2650045

Zentralblatt MATH identifier
1197.60089

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C21: Dynamic continuum models (systems of particles, etc.)

Keywords
Coagulating particle systems hydrodynamic limit Smoluchowski’s equations

Citation

Armendáriz, Inés. Brownian coagulation and a version of Smoluchowski’s equation on the circle. Ann. Appl. Probab. 20 (2010), no. 2, 660--695. doi:10.1214/09-AAP633. https://projecteuclid.org/euclid.aoap/1268143436


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