Scaling analysis of galaxy distribution in the Las Campanas Redshift Survey data

The Las Campanas Redshift Survey data are used to investigate structures of the galaxy number distribution. We construct two volume-limited samples wi th sizes of 113 x 113 and 126 x 126 h(-1) Mpc, and calculate the second- to ninth-order moments with the count-in-cell method. The galaxy distribution at greater than or equal to 30 h(-1) Mpc is found to be statistically homo geneous. On the other hand. we find a multifractal scaling at < 30 h(-1) Mp c. From the scaling exponent, we obtain the generalized dimension. which de creases from 2 toward 1 as the order is increased from 2 to 9. Galaxies are known to lie. around voids, in planar structures with filamentary dense re gions. The present result indicates that these void-filament structures are predominant up to 30 h(-1) Mpc. Statistically, they appear to he the large st-scale significant structures in the Universe.