Analysis of diffusion trajectories of anisotropic objects

We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure based on the gyration tensor, and obtain its analytic expression exactly. Its efficiency and statistical convergence are examined in comparison with the fourth cumulant of particle displacement. We find that the estimation of diffusion constants based on the gyration measure is more efficient than analysis adopting the fourth cumulant.