  Poissonian ensembles of Markov loops on a finite graph define a random graph
process in which the addition of a loop can merge more than two connected
components. We study Markov loops on the complete graph derived from a simple
random walk killed at each step with a constant probability. Using a component
exploration procedure, we describe the asymptotic distribution of the connected
component size of a vertex at a time proportional to the number of vertices,
show that the largest component size undergoes a phase transition and establish
the coagulation equations associated to this random graph process.
