Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve
  with Shannon entropy
  We analyze a set of volume limited samples from SDSS DR12 to quantify the
degree of inhomogeneity at different length scales using Shannon entropy. We
find that the galaxy distributions exhibit a higher degree of inhomogeneity as
compared to a Poisson point process at all length scales. Our analysis
indicates that signatures of inhomogeneities in the galaxy distributions
persist at least upto a length scale of $120 \, h^{-1}\, {\rm Mpc}$. The galaxy
distributions appear to be homogeneous on a scale of $140 \, h^{-1}\, {\rm
Mpc}$ and beyond. Analyzing a set of mock galaxy samples from a semi analytic
galaxy catalogue from the Millennium simulation we find a scale of transition
to homogeneity at $\sim 100 \, h^{-1}\, {\rm Mpc}$.
