  Experiments involving the two-dimensional passive diffusion of colloidal
boomerangs tracked off their centre of mobility have shown striking
non-Gaussian tails in their probability distribution function [Chakrabarty et
al., Soft Matter 12, 4318 (2016)]. This in turn can lead to anomalous diffusion
characteristics, including mean drift. In this paper, we develop a general
theoretical explanation for these measurements. The idea relies on calculating
the two-dimensional probability densities at the centre of mobility of the
particle, where all distributions are Gaussian, and then transforming them to a
different reference point. Our model clearly captures the experimental results,
without any fitting parameters, and demonstrates that the one-dimensional
probability distributions may also exhibit strongly non-Gaussian tops. These
results indicate that the choice of tracking point can cause a considerable
departure from Gaussian statistics, potentially causing some common modelling
techniques to fail.
