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An information theory based search for homogeneity on the largest accessible scale

We analyze the SDSS DR12 quasar catalogue to test the large-scale smoothness in the quasar distribution. We quantify the degree of inhomogeneity in the quasar distribution using information theory based measures and find that the degree of inhomogeneity diminishes with increasing length scales which finally reach a plateau at $\sim 250 \, h^{-1}\, {\rm Mpc}$. The residual inhomogeneity at the plateau is consistent with that expected for a Poisson point process. Our results indicate that the quasar distribution is homogeneous beyond length scales of $250 \, h^{-1}\, {\rm Mpc}$.