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We analyze a set of volume limited sample of galaxies from the SDSS to studythe issue of cosmic homogeneity. We use the Renyi entropy of different order toprobe the inhomogeneties present in the galaxy distributions. We also calculatethe Renyi diveregence to quantify the deviations of the galaxy distributionfrom a homogeneous Poisson distribution on different length scales. Weseparately carry out the analysis using the overlapping spheres and theindependent voxels. Our analysis suggests that the scale of homogeneity isunderestimated in the smaller galaxy samples due to the suppression ofinhomogeneities by the overlapping of the measuring speheres. We find that ananalysis with the independent voxels and/or use of a significantly largergalaxy sample can help to circumvent or mitigate this problem. Combining theresults from these analyses, we find that the galaxy distribution in the SDSSbecomes homogeneous on a length scale beyond $140 \, h^{-1}\, {\rm Mpc}$.

Testing homogeneity of the galaxy distribution in the SDSS using Renyi entropy