On the Condensation and fluctuations in reversible coagulation-fragmentation models

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 one 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 \emph{i.i.d.} according to the normalized equilibrium state of the limit hydrodynamic differential equation. Conditions for the normal fluctuations and the $\alpha$-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.