Abstract
L\'evy walks are random walks in which the distribution of step length does not decay exponentially and the velocity of the moving particle is finite. Building on earlier concepts, they reconcile anomalously fast diffusion with a finite propagation speed and have applications that range from basic statistical mechanics and transport theory to optics, cold atom dynamics, and biophysics. This review gives an introduction to this important class of models and discusses applications in both physics and biology.
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