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Coagulation and diffusion: a probabilistic perspective on the Smoluchowski PDE. (English) Zbl 1384.82010

This is a survey on various questions related to diffusive coagulating systems. More especially here, the author deals with the Smoluchowski coagulation-diffusion partial differential equation (PDE), and the author details how the latter can be derived in a kinetic limit from a set of microscopic random models of diffusing particles which are mutually coagulating two at a time. The survey is expanded around a main theorem which describes the evolution of the density of particles of different masses in the limit of large particles. In this paper, typically we are going from microscopic particles to macroscopic systems.

MSC:

82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q84 Fokker-Planck equations
60J65 Brownian motion
35Q20 Boltzmann equations
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