  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
inter-disk collisions. The velocity auto-correlation 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
square displacements and discuss distinctions between its mean and mode. These
well-controlled experimental data can serve for validating statistical tools
developed for the analysis of single-particle trajectories in microbiology.
