  Anisotropic diffusion processes emerge in various fields such as transport in
biological tissue and diffusion in liquid crystals. In such systems, the motion
is described by a diffusion tensor. For a proper characterization of processes
with more than one diffusion coefficient an average description by the mean
squared displacement is often not sufficient. Hence, in this paper, we use the
distribution of diffusivities to study diffusion in a homogeneous anisotropic
environment. We derive analytical expressions of the distribution and relate
its properties to an anisotropy measure based on the mean diffusivity and the
asymptotic decay of the distribution. Both quantities are easy to determine
from experimental data and reveal the existence of more than one diffusion
coefficient, which allows the distinction between isotropic and anisotropic
processes. We further discuss the influence on the analysis of projected
trajectories, which are typically accessible in experiments. For the
experimentally relevant cases of two- and three-dimensional anisotropic
diffusion we derive specific expressions, determine the diffusion tensor,
characterize the anisotropy, and demonstrate the applicability for simulated
trajectories.
