Statistical analysis of random trajectories of vibrated disks: Towards a macroscopic realization of Brownian motion

We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost Gaussian, with slight deviations at large increments caused by interdisk collisions. The velocity autocorrelation function takes both positive and negative values at short lag times but rapidly vanishes. We compare the empirical and theoretical distributions of time-averaged mean-squared displacements and discuss distinctions between their mean and mode. These well-controlled experimental data can serve for validating various statistical tools developed for the analysis of single-particle trajectories in microbiology.