2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97999The distribution of the initial very short-time displacements of a single particle is considered for a class of classical systems with Gaussian initial velocity distributions and arbitrary initial particle positions. A very brief sketch is given of a rather intricate and lengthy proof that for this class of systems the nth order cumulants behave as t^{2n} for all n>2, rather than as t^{n}. We also briefly discuss some physical consequences for liquids.Short 8 page pedagogical review of cond-mat/0505734 for Proc. of "News, Expectations and Trends in Statistical Physics", Crete 2005Statistical Mechanicstext