Nature of clustering in the Las Campanas redshift survey

We have carried out a multi-fractal analysis of the distribution of galaxies in the three Northern slices of the Las Campanas Redshift Survey (LCRS). Our method takes into account the selection effects and the complicated geometry of the survey. In this analysis we have studied the scaling properties of the distribution of galaxies on length scales from 20h−1Mpc to 200h−1Mpc. Our main results are: (1) the distribution of galaxies exhibits a multi-fractal scaling behaviour over the scales 20h−1Mpc to 80h−1Mpc, and, (2) it is consistent with a homogeneous distribution on the scales 80h−1Mpc to 200h−1Mpc. We conclude that the distribution of galaxies in the LCRS is consistent with the universe being homogeneous at large scales and the transition to homogeneity occurs somewhere in the range 80h−1Mpc to 100h−1Mpc.