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We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a Maxwell-Boltzmann distribution. The PDFs are symmetric around zero velocity and show a Gaussian core and exponential tails over more than six orders of magnitude of probability. Following the excellent agreement of our theory and simulation data, we demonstratedoi:10.1209/0295-5075/83/30001 fatcat:34wvdnns5vfezdb6u5od333ts4