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On the Condensation and fluctuations in reversible coagulation–fragmentation models

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  • Sun, Wen

Abstract

We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation–fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the associated balance equation satisfy a subexponential tail condition, there is a single giant particle that corresponds to the missing mass in the macroscopic limit. We also show that in this case, the rest of the particles are asymptotically i.i.d according to the normalised equilibrium state of the limit hydrodynamic differential equation. Conditions for the normal fluctuations and the α-stable fluctuations around the condensed mass are given. We obtain the large deviation principle for the empirical measure of the masses of the particles at equilibrium as well.

Suggested Citation

  • Sun, Wen, 2026. "On the Condensation and fluctuations in reversible coagulation–fragmentation models," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002728
    DOI: 10.1016/j.spa.2025.104828
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    References listed on IDEAS

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    1. Armendáriz, Inés & Loulakis, Michail, 2011. "Conditional distribution of heavy tailed random variables on large deviations of their sum," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1138-1147, May.
    2. E. Hingant & R. Yvinec, 2017. "Deterministic and Stochastic Becker–Döring Equations: Past and Recent Mathematical Developments," Springer Books, in: David Holcman (ed.), Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, pages 175-204, Springer.
    3. Richard Durrett & Boris L. Granovsky & Shay Gueron, 1999. "The Equilibrium Behavior of Reversible Coagulation-Fragmentation Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 447-474, April.
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