Correlation coefficients r₁ and r₂ measured from the halo catalogs in the subcubes of the Millennium Simulation, using the LS estimator, where we slice the simulation volume into 1000 subcubes for the left panel and 125 for the right one, and the random catalog for each subcube contains 5000 halos. In both cases, we measure ξ at lags of separation Δs = 5 h^-1Mpc, and use all halo pairs with pair separations of 0 to 2 h^-1Mpc to compute ξ₀. The red dots show the 1000 (125) realizations, while the black lines are iso-density contours that contain the given percentages of the realizations. The upper and lower constraints r_2u,l(r₁), computed individually for each realization of r₁, are shown as blue lines.