# The non-Gaussian tops and tails of diffusing boomerangs

## TL;DR

This paper provides a theoretical explanation for the non-Gaussian tails observed in the diffusion of colloidal boomerangs, showing how tracking points influence statistical behavior and modeling accuracy.

## Contribution

Develops a general theoretical model explaining non-Gaussian diffusion tails in colloidal boomerangs based on tracking point transformations.

## Key findings

- Model accurately reproduces experimental non-Gaussian tails
- Tracking point choice significantly affects diffusion statistics
- Gaussian distributions at the center of mobility transform into non-Gaussian tails

## Abstract

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.