The Non-Uniform Distribution of Galaxies from Data of the SDSS DR7
  Survey
  We have analyzed the spatial distribution of galaxies from the release of the
Sloan Digital Sky Survey of galactic redshifts (SDSS DR7), applying the
complete correlation function (conditional density), two-point conditional
density (cylinder), and radial density methods. Our analysis demonstrates that
the conditional density has a power-law form for scales lengths 0.5-30 Mpc/h,
with the power-law corresponding to the fractal dimension D = 2.2+-0.2; for
scale lengths in excess of 30 Mpc/h, it enters an essentially flat regime, as
is expected for a uniform distribution of galaxies. However, in the analysis
applying the cylinder method, the power-law character with D = 2.0+-0.3
persists to scale lengths of 70 Mpc/h. The radial density method reveals
inhomogeneities in the spatial distribution of galaxies on scales of 200 Mpc/h
with a density contrast of two, confirming that translation invariance is
violated in the distribution of galaxies to 300 Mpc/h, with the sampling depth
of the SDSS galaxies being 600 Mpc/h.
