  The Marcus-Lushnikov process is a finite stochastic particle system, in which
each particle is entirely characterized by its mass. Each pair of particles
with masses $x$ and $y$ merges into a single particle at a given rate $K(x,y)$.
Under certain assumptions, this process converges to the solution to
Smoluchowski equation, as the number of particles increases to infinity. The
Marcus-Lushnikov process gives at each time the distribution of masses of the
particles present in the system, but does not retain the history of formation
of the particles. In this paper, we set up a historical analogue of the
Marcus-Lushnikov process (built according the rules of construction of the
usual Markov-Lushnikov process) each time giving what we call the historical
tree of a particle. The historical tree of a particle present in the
Marcus-Lushnikov process at a given time $t$ encodes information about the
times and masses of the coagulation events that have formed that particle. We
prove a law of large numbers for the empirical distribution of such historical
trees. The limit is a natural measure on trees which is constructed from a
solution to Smoluchowski coagulation equation.
