Testing isotropy in the Two Micron All-Sky redshift survey with
  information entropy
  We use information entropy to test the isotropy in the nearby galaxy
distribution mapped by the Two Micron All-Sky redshift survey (2MRS). We find
that the galaxy distribution is highly anisotropic on small scales. The radial
anisotropy gradually decreases with increasing length scales and the observed
anisotropy is consistent with that expected for an isotropic Poisson
distribution beyond a length scale of $90 \, h^{-1}\, {\rm Mpc}$. Using mock
catalogues from N-body simulations, we find that the galaxy distribution in the
2MRS exhibits a degree of anisotropy compatible with that of the $\Lambda$CDM
model after accounting for the clustering bias of the 2MRS galaxies. We also
quantify the polar and azimuthal anisotropies and identify two directions
$(l,b)=(150^{\circ}, -15^{\circ})$, $(l,b)=(310^{\circ},-15^{\circ})$ which are
significantly anisotropic compared to the other directions in the sky. We
suggest that their preferential orientations on the sky may indicate a possible
alignment of the Local Group with two nearby large scale structures. Despite
the differences in the degree of anisotropy on small scales, we find that the
galaxy distributions in both the 2MRS and the $\Lambda$CDM model are isotropic
on a scale of $90 \, h^{-1}\, {\rm Mpc}$.
