Display of the correlation coefficient between the non-linear density and the negative divergence of the non-linear velocity field, θ ≡ −∇ ⋅ v. The red line is the ensemble average over the posterior distribution of the cross-correlation and the shaded dark red area is the one standard deviation according to the mean of that cross-correlation derived from the same distribution obtained by BORG. The green and shaded green region is the result of computing the same quantities on 80 random realizations. Apart from very minor differences, the two curves are on top of each other, which can be expected as the physical model is the same in both cases. The vertical grey band on the right side indicate the resolution limit of the BORG reconstruction. The correlation reaches asymptotically one for the largest scales (small k values). The red line is reaching a value of 99% for the largest probed mode. As expected, this cross-correlation goes to zero at small scales (high k value).