Testing homogeneity of the galaxy distribution in the SDSS using Renyi
  entropy
  We analyze a set of volume limited sample of galaxies from the SDSS to study
the issue of cosmic homogeneity. We use the Renyi entropy of different order to
probe the inhomogeneties present in the galaxy distributions. We also calculate
the Renyi diveregence to quantify the deviations of the galaxy distribution
from a homogeneous Poisson distribution on different length scales. We
separately carry out the analysis using the overlapping spheres and the
independent voxels. Our analysis suggests that the scale of homogeneity is
underestimated in the smaller galaxy samples due to the suppression of
inhomogeneities by the overlapping of the measuring speheres. We find that an
analysis with the independent voxels and/or use of a significantly larger
galaxy sample can help to circumvent or mitigate this problem. Combining the
results from these analyses, we find that the galaxy distribution in the SDSS
becomes homogeneous on a length scale beyond $140 \, h^{-1}\, {\rm Mpc}$.
