Abstract
We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles are within a distance of order ε. Our model is macroscopically described by an inhomogeneous Smoluchowski’s equation in the low ε limit provided that the initial number of particles N is of order |log ε|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low ε limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation.
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Communicated by H. Spohn
This work is supported in part by NSF grant DMS-0707890.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ranjbar, M., Rezakhanlou, F. Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles. Commun. Math. Phys. 296, 769–826 (2010). https://doi.org/10.1007/s00220-010-1016-9
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DOI: https://doi.org/10.1007/s00220-010-1016-9