Threshold biasing of a Gaussian random field gives a linear amplification of the reduced two-point correlation function at large distances. We show that for standard cosmological models this does not translate into a linear amplification of the power spectrum (PS) at small k. For standard cold dark matter-type models, the "turnover" at small k of the original PS disappears in the PS of the biased field for the physically relevant range of threshold parameters nu. In real space, this difference is manifest in the asymptotic behavior of the normalized mass variance in spheres of radius R, which changes from the "superhomogeneous" behavior sigma(2)(R) similar to R-4 to a Poisson-like behavior sigma(nu)(2) (R) similar to R-3. This qualitative change results from the intrinsic stochasticity of the threshold sampling. While our quantitative results are specific to the simplest threshold biasing model, we argue that our qualitative conclusions should be valid generically for any biasing mechanism involving a scale-dependent amplification of the correlation function. One implication is that the real-space correlation function will be a better instrument to probe for the underlying Harrison-Zeldovich spectrum in the distribution of visible matter, as the characteristic asymptotic negative power-law xi(r) similar to -r(-4) tail is undistorted by biasing.
Durrer, R., Gabrielli, A., Joyce, M., Sylos Labini, F. (2003). Bias and the power spectrum beyond the turnover. THE ASTROPHYSICAL JOURNAL, 585(1), L1-L4 [10.1086/374208].