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A Functional Central Limit Theorem for the Becker–Döring Model

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Abstract

We investigate the fluctuations of the stochastic Becker–Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

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Acknowledgements

The author thanks two anonymous referees for their comments and references that have been very helpful to clarify several aspects of this paper. The author also would like to express her gratitude to her advisor Professor Philippe Robert for valuable discussions. The author’s work is supported by the grant from Foundation Sciences Mathématiques de Paris (FSMP), overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Reference: ANR-10-LABX-0098).

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    Wen Sun

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Sun, W. A Functional Central Limit Theorem for the Becker–Döring Model. J Stat Phys 171, 145–165 (2018). https://doi.org/10.1007/s10955-018-1993-1

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  • DOI: https://doi.org/10.1007/s10955-018-1993-1

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