The scale of homogeneity in the Las Campanas Redshift Survey

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/h) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/h, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data. Subject headings: galaxies: clusters: general large-scale structure of universe Following seminal work of Pietronero and coworkers, (see e.g. Pietronero et al. 1996), the possibility of a large-scale fractal distribution of the galaxies has been investigated by various authors. In the current literature, however, there are several conflicting estimates of the largest scale at which the galaxy distribution can be approximated by a fractal, ranging from a few Megaparsecs (e.g. Peebles 1993), to 20 Mpc/h (Davis 1996), to 40 Mpc/h (Cappi et al. 1998), up to more than 100 Mpc/h (e.g. Pietronero et al. 1996). A fractal distribution with dimension D is characterized by the property that the correlation function