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. 
David Alonso, Ana Isabel Salvador, Francisco Javier S\'anchez, Maciej   Bilicki, Juan Garc\'ia-Bellido, Eusebio S\'anchez
astro-ph.CO