Homogeneity and isotropy in the 2MASS Photometric Redshift catalogue
  Using the 2MASS Photometric Redshift catalogue we perform a number of
statistical tests aimed at detecting possible departures from statistical
homogeneity and isotropy in the large-scale structure of the Universe. Making
use of the angular homogeneity index, an observable proposed in a previous
publication, as well as studying the scaling of the angular clustering and
number counts with magnitude limit, we place constraints on the fractal nature
of the galaxy distribution. We find that the statistical properties of our
sample are in excellent agreement with the standard cosmological model, and
that it reaches the homogeneous regime significantly faster than a class of
fractal models with dimensions $D<2.75$. As part of our search for systematic
effects, we also study the presence of hemispherical asymmetries in our data,
finding no significant deviation beyond those allowed by the concordance model.
