Power-spectrum simulations of radial redshift distributions
  On the base of the simplest model of a modulation of 3D Gaussian field in
$k$-space we produce a set of simulations to bring out the effects of a
modulating function $f_{\rm mod} (k)=f_1 (k) + f_2 (k)$ on power spectra of
radial (shell-like) distributions of cosmological objects, where a model
function $f_1 (k)$ reproduces the smoothed power spectrum of underlying 3D
density fluctuations, while $f_2 (k)$ is a wiggling function imitating the
baryon acoustic oscillations (BAO). It is shown that some excess of
realizations of simulated radial distributions actually displays
quasi-periodical components with periods about a characteristic scale $2\pi/k
\sim 100~h^{-1}$~Mpc detected as power-spectrum peaks in vicinity of the first
maximum of the modulation function $f_2 (k)$. We revised our previous
estimations of the significance of such peaks and found that they were largely
overestimated. Thereby quasi-periodical components appearing in some radial
distributions of matter are likely to be stochastic (rather than
determinative), while the amplitudes of the respective spectral peaks can be
quite noticeable. They are partly enhanced by smooth part of the modulating
function $f_1(k)$ and, to a far lesser extent, by effects of the BAO (i.e.
$f_2(k)$). The results of the simulations match quite well with statistical
properties of the radial distributions of the brightest cluster galaxies
(BCGs).
