  We consider an exploration algorithm where at each step, a random number of
items become active while related items get explored. Given an initial number
of items $N$ growing to infinity and building on a strong homogeneity
assumption, we study using scaling limits of Markovian processes statistical
properties of the proportion of active nodes in time. This is a companion paper
that rigorously establishes the claims and heuristics presented in [5].
  [5] Jaron Sanders, Matthieu Jonckheere, and Servaas Kokkelmans.
Sub-Poissonian statistics of jamming limits in Rydberg gases. 2015. To appear.
