2013/08/19 by Lemaire, Sophie
#05C80 #60C05 #60J80 #82C31 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1308.4100
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.