The Monte Carlo criticality simulation of decoupled systems, as for instance in large reactor cores, has been a challenging issue for a long time. In particular, due to limited computer time resources, the number of neutrons simulated per generation is still many order of magnitudes below realistic statistics, even during the start-up phases of reactors. This limited number of neutrons triggers a strong clustering effect of the neutron population that affects Monte Carlo tallies. Below a certain threshold, not only is the variance affected but also the estimation of the eigenvectors. In this paper we will build a time-dependent diffusion equation that takes into account both spatial correlations and population control (fixed number of neutrons along generations). We will show that its solution obeys a traveling wave dynamic, and we will discuss the mechanism that explains this biasing of local tallies whenever leakage boundary conditions are applied to the system. © 2017