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We propose a macroscopic realization of planar Brownian motion by verticallyvibrated disks. We perform a systematic statistical analysis of many randomtrajectories of individual disks. The distribution of increments is shown to bealmost Gaussian, with slight deviations at large increments caused byinter-disk collisions. The velocity auto-correlation function takes bothpositive and negative values at short lag times but rapidly vanishes. Wecompare the empirical and theoretical distributions of time averaged meansquare displacements and discuss distinctions between its mean and mode. Thesewell-controlled experimental data can serve for validating statistical toolsdeveloped for the analysis of single-particle trajectories in microbiology.

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