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.