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On levy-walk model for correlations in spatial galaxy distribution

One of important problems complicating the extraction of information from cosmological surveys, is necessity to supplement observational data subtracted of foreground or for some (i.e. technical) reasons removed from the survey. This particularly affects the extraction of information from the largest observable scales. Maximum-likelihood estimators are not quite applicable for reconstructing the full-sky because of non-Caussian character of observed matter distribution. To solve this problem, many authors modify implementations of such estimators which are robust to the leakage of contaminants from within masked regions. The trouble arises from the need to satisfy the cosmological principle of an arbitrary choice of the reference frame and long-distant correlations in spatial galaxy distribution observed. We are going to discuss here one а such approach and to show some results of its application. The discussion about homogeneity (or inhomogeneity) of the large-scale visible matter distribution in the Universe is attracting the attention of both the astronomers and theoreticians of cosmology.1–4 In recent years the more complete and deeper galaxy surveys become available,5,6 however, this does not eliminate the question about fractality of the large-scale structure. The fractal concept, introduced by Mandelbrot,7 applied to the galaxy distribution means the presence of the overdence regions and voids extending to all scales, at least to those could be reached by now. Mathematically, it formulates as