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Journal Articles Journal of Statistical Physics Year : 2018

The Becker-Doring Process: Pathwise Convergence and Phase Transition Phenomena

Erwan Hingant

Abstract

In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model.In this note, we prove alaw of large numbersfor an infinite chemical reactionnetwork for phase transition problems called the stochastic Becker-Döring process.Under a general condition on the rate constants we show the convergence in lawand pathwise convergence of the process towards the deterministic Becker-Döringequations. Moreover, we prove that the non-equilibrium potential, associated to thestationary distribution of the stochastic Becker-Döring process, approaches the rela-tive entropy of the deterministic limit model. Thus, the phase transition phenomenathat occurs in the infinite dimensional deterministic modelis also present in the finitestochastic model.
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hal-01852561 , version 1 (01-08-2018)

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Erwan Hingant, Romain Yvinec. The Becker-Doring Process: Pathwise Convergence and Phase Transition Phenomena. Journal of Statistical Physics, 2018, 177 (5), pp.506-527. ⟨10.1007/s10955-019-02377-2⟩. ⟨hal-01852561⟩
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