Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles |
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Authors: | Mojtaba Ranjbar Fraydoun Rezakhanlou |
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Affiliation: | (1) Courant Institute, Warren Weaver Hall, 251 Mercer Street, New York, NY 10012, USA;(2) Department of Mathematics, University of California, Berkeley California, 94720-3840, USA |
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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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