Correlation function of quasars in real and redshift space from the
  Sloan Digital Sky Survey Data Release 7
  We analyze the quasar two-point correlation function (2pCF) within the
redshift interval $0.8<z<2.2$ using a sample of 52303 quasars selected from the
recent 7th Data Release of the Sloan Digital Sky Survey. Our approach to 2pCF
uses a concept of locally Lorentz (Fermi) frame for determination of the
distance between objects and permutation method of the random catalogue
generation. Assuming the spatially flat cosmological model with given
$\Omega_{\Lambda}=0.726$, we found that the real-space 2pCF is fitted well with
the power-low model within the distance range $1<\sigma<35$ $h^{-1}$ Mpc with
the correlation length $r_{0}=5.85\pm0.33$ $h^{-1}$ Mpc and the slope
$\gamma=1.87\pm0.07$. The redshift-space 2pCF is approximated with
$s_{0}=6.43\pm0.63$ $h^{-1}$ Mpc and $\gamma=1.21\pm0.24$ for $1<s<10$ $h^{-1}$
Mpc, and $s_{0}=7.37\pm0.81$ $h^{-1}$ Mpc and $\gamma=1.90\pm0.24$ for
$10<s<35$ $h^{-1}$ Mpc. For distances $s>10\,h^{-1}$ Mpc the parameter
describing the large-scale infall to density inhomogeneities is
$\beta=0.63\pm0.10$ with the linear bias $b=1.44\pm0.22$ that marginally
(within 2$\sigma$) agrees with the linear theory of cosmological perturbations.
We discuss possibilities to obtain a statistical estimate of the random
component of quasars velocities (different from the large-scale infall). We
note rather slight dependence of quasars velocity dispersion upon the 2pCF
parameters in the region $r<2$ Mpc.
