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Astron. Astrophys. 351, 405-412 (1999)

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6. Conclusion

Here we present a method for carrying out the multi-fractal analysis of both magnitude and volume limited subsamples of the LCRS. Our method takes into account the various selection effects and the complicated geometry of the survey.

We first apply our method to random realizations of the LCRS subsamples for which we ideally expect a flat spectrum of generalized dimensions with [FORMULA]. Our analysis gives a nearly flat spectrum with [FORMULA] on large scales. The deviation from the expected value includes statistical errors arising from the finite number of galaxies and systematic errors arising from our treatment of the selection effects and the complicated geometry. The fact that the errors are small clearly shows that our method correctly accounts for these effects.

Our analysis of the actual data shows the existence of two different regimes and the distribution of galaxies on scales [FORMULA] shows clear indication of a multi-fractal scaling behaviour. On large scales [FORMULA] we find a nearly flat spectrum with [FORMULA]. This is consistent with our analysis of the random realizations which have been constructed from a homogeneous underlying distribution of galaxies.

Based on the above analysis we conclude that the distribution of galaxies in the Las Campanas Redshift Survey is consistent with homogeneous distribution at large scales with the transition to homogeneity occurring somewhere around [FORMULA] to [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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