  In this note, we study an infinite reaction network called the stochastic
Becker-D\"oring process, a sub-class of the general coagulation-fragmentation
models. We prove pathwise convergence of the process towards the deterministic
Becker-D\"oring equations which improves classical tightness-based results.
Also, we show by studying the asymptotic behavior of the stationary
distribution, that the phase transition property of the deterministic model is
also present in the finite stochastic model. Such results might be interpreted
closed to the so-called gelling phenomena in coagulation models. We end with
few numerical illustrations that support our results.
