Effect of observational holes in fractal analysis of galaxy survey masks
  Observations reveal that the Universe has a hierarchy of galaxy clustering
with transition to homogeneity on large scales according to the $\Lambda$CDM
model. On the other hand some observational estimates suggest a multifractal
behavior where galactic clustering is based on generalization of the
correlation dimension. We study the influence of veto areas on fractal
measurements in masks of galaxy surveys. We investigate if these holes can
produce fractal behaviors or modify the scale of cosmic homogeneity. From the
footprint of BOSS-DR12, we build a homogeneous sample following the radial
selection function for 73,412 points limited to the redshift range
$0.002<z<0.2$. Different percentages of observational holes were created
cumulatively in RA and dec on the sample. For the synthetic sample and for a
real sample of galaxies we determined the fractal dimension $D_q(r)$ in the
range $2\leq q\leq6$ using the sliding window technique to characterize the
spatial point distribution. Our results show that generalized dimension varies
with the scale, for low scales there are a fractal behavior with fluctuations
for all hole percentages studied and for larger scales than 113 Mpc/h the
statistical homogeneity is achieved in concordance with other analysis. We find
that observational holes cause a shift in the homogeneity scale $r_H$, in
particular for synthetic samples with percentages of holes between 0-10% the
homogeneity scale is reached at $(83\pm1)$Mpc/h while the fractal dimension
changes as $2.83^{\pm0.09}\leq D_q\leq2.855^{\pm0.09}$. For synthetic samples
with percentages of holes greater than 10%, we find that the value of $r_H$
increases proportionally. Consequently future results about homogeneity scale
based in fractal analyses must be corrected by observational holes and regions
of incompleteness in the geometry of the galaxy catalogue if the size of the
veto mask is significant.
