Variance σ₈ as a function of scale factor a_uni for P‐sampled ICs (left) and ξ‐sampled ICs (right). The ensembles had ﹩L=50\ h^{-1}\ \mathrm{Mpc}\,﹩, ﹩N=32^{3}﹩. For a given a_uni, I calculated σ₈ with a Monte Carlo integrator for each realization. The light green region shows the range of σ₈ for the 100 realizations. The purple region shows the 68.3% confidence region on individual realizations, and the black "line" shows the 68.3% confidence region for the ensemble average. The linear theory expectation of σ₈’s evolution is plotted as the bottom red line. The middle red line is the theoretical value with the expected lattice contribution added in quadrature; the top red line is the theoretical value with the appropriate Poisson contribution added in quadrature. The bottom panels plot the same information as the top panels, except using a linear scale, which makes clearer the discrepancy between the theoretical and calculated evolution of σ₈ in the P‐sampled case, and the agreement in the ξ‐sampled case. In the bottom panels I have also plotted, with blue lines, 10 of the 100 realizations to show qualitatively individual errors due to the Monte Carlo integrator. I chose the same 10 random seeds for both the P‐ and ξ‐sampled cases. These individual evolution tracks also show qualitatively that a realization with a small value of σ₈ early in the simulation has a small value later in the simulation as well.