## 5. Results and discussionWe first discuss our analysis of the mock subsamples. Since the effect of the selection function and the geometry of the slices have both been included in generating these subsamples, our analysis of these subsamples allows us to check how well these effects are being corrected for. In the ideal situation for all the mock subsamples we should recover a flat spectrum of generalized dimensions with corresponding to a homogeneous point distribution. The actual results of the multi-fractal analysis of the mock subsamples are presented below where we separately discuss the behaviour of at small scales and at large scales . The results for mock versions of the subsample d-12.1 are shown in Fig. 1. This is a magnitude limited subsample from a slice that has only 112 fibre fields and it contains the largest number of galaxies. We get a nearly flat spectrum with corresponding to a homogeneous point distribution at both small and large scales. Similar results are also obtained for mock versions of the other subsamples of the slice.
The analysis of mock versions of the subsample d-03.1 which
contains both 112 and 50 fibre fields gives a spectrum with a weak
We thus find that the analysis is most effective for the subsample
from the slice where
shows very little We next discuss our analysis of the actual data. The analysis of
the curves corresponding to versus
We find that at small scales the plots of
versus At large scales the behaviour of the generalized dimension
is quite different. For the
subsample d-12.1 the spectrum shows a weak The work presented here contains significant improvements on the earlier work of Amendola & Palladino (1999) on two counts and these are explained below: (1) Unlike the earlier work which has analyzed volume limited subsamples of one of the slices () of the LCRS we have analyzed both volume and magnitude limited subsamples of all the three northern slices of the LCRS. The magnitude limited samples contain more than four times the number of galaxies in the volume limited samples and they extend to higher redshifts. This allows us to make better use of the data in the LCRS to improve the statistical significance of the results and to probe scales larger than those studied in the previous analysis. (2) We have calculated the full spectrum of generalized dimensions which has information about the nature of clustering in different environments. The integrated conditional density used by the earlier workers is equivalent to a particular point on the spectrum and it does not fully characterize the scaling properties of the distribution of galaxies. © European Southern Observatory (ESO) 1999 Online publication: November 3, 1999 |