  The investigation of correlations in Monte Carlo power iteration has been
long dominated by the question of generational correlations and their effects
on the estimation of statistical uncertainties. More recently, there has been a
growing interest in spatial correlations, prompted by the discovery of neutron
clustering. Despite several attempts, a comprehensive framework concerning how
Monte Carlo sampling strategies, population control and variance reduction
methods affect the strength of such correlations is still lacking. In this
work, we propose a set of global and local (i.e., space-dependent) tallies that
can be used to characterize the impact of correlations. These tallies encompass
the Shannon entropy, the pair distance, the normalized variance and the Feynman
moment. In order to have a clean, yet fully meaningful setting, we carry out
our analysis in a few homogeneous and heterogeneous benchmark problems of
varying dominance ratio. Several classes of collision sampling strategies,
population control and variance reduction techniques are tested, and their
relative advantages and drawbacks are assessed with respect to the proposed
tallies. The major finding of our study is that branchless collisions, which
suppress the emergence of branches in neutron histories, also considerably
reduce the effects of correlations in most of the explored configurations.
