Top panels show 100 individual realizations’ values of σ₈ for ﹩L=50\ h^{-1}\ \mathrm{Mpc}\,﹩, ﹩N=32^{3}﹩ for ﹩z=38.81﹩ (left) and ﹩z=5.67﹩ (right), with particle positions generated with the second‐order Lagrangian perturbation theory initial conditions code. The green open circles are for P‐sampled ICs; the blue filled circles are for ξ‐sampled ICs, and the red triangles are for ξ‐sampled ICs with the DC mode artificially set to zero. All three cases used the same 100 random number seeds. A thin black line connects the range of values for each realization. The values of Δ₀ from the ξ‐sampled case serve as the abscissae. Values of σ₈ are accurate to 0.25%. The bottom panels plot the 100 realizations’ values of ﹩\sigma ^{2}_{8,\,\mathrm{DC}\,}=\sigma ^{2}_{8,\,\xi - \mathrm{sampled}\,}-\sigma ^{2}_{8,\, P- \mathrm{sampled}\,}﹩. The expected value of ﹩\Delta ^{2}=\left[\overline{D}( a) \Delta _{0}\right]^{2}﹩ is also shown.