A large-deviations principle (LDP) is derived for the state, at fixed time, of the multiplicative coalescent in the large particle number limit.
The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic.
In particular, it clearly captures the well known gelation phase transition given by the formation of a particle
containing a positive fraction of the system mass at time t=1.
Via a standard map of the multiplicative coalescent onto a time-dependent
version of the Erd\H{o}s-R\'enyi random graph, our results can also be rephrased
as an LDP for the component sizes in that graph.
Our proofs rely on estimates and asymptotics for the probability that smaller Erd\H{o}s-R\'enyi graphs are connected
