This work presents a two-dimensional phenomenological Monte Carlo toy model for studying how weak spatial correlations in primordial black hole (PBH) seed distributions affect hierarchical merger growth. We compare spatially correlated perturbed-lattice initial conditions with uncorrelated random initial conditions under identical simplified merger dynamics with an effective expansion suppression. The simulations show that correlated seed placement produces fewer surviving PBHs, larger maximum remnant masses, and higher runaway growth probabilities in the low-expansion regime. The results should be interpreted as a proof-of-concept study rather than a direct cosmological prediction.
tukka (Sat,) studied this question.