Geometrical constraints, boundary conditions and interactions are expected to modify standard classical random motion. Two examples are given: (i) motion of a particle in a long narrow pipe, which can be viewed as a sequence of clusters of small erratic steps separated by long-distance jumps, strongly reminiscent of a Lévy walk at least on a pictorial level. (ii) 1d diffusion of a set of N particles with a hard-core contact interaction. In the first case, according to the nature of the bounces (elastic random, thermal, soft…), the mean square dispersion displays a large variety of asymptotic behaviours: t2/ln t, tμ … In most cases, the behaviour is superdiffusive; For the N interacting particles on the line, the kth moment of the one-body reduced coordinate distributions behaves as tk/2 at all times. In particular, although ordinary diffusion always occurs, the diffusion constant D strongly depends in a non-intuitive way upon the number N of interacting particles; for the borderline particle, D(N) decreases as 1/ln N whereas for the central one, D(N) decreases as N−1.
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