Cooling gases with Levy flights: using the generalized central limit theorem in physics

In the last ten years, the generalized central limit theorem established by Paul Levy in the thirties has been found more and more relevant in physics. Physicists call 'Levy flights' random walks for which the probability density of the jump lenghts $x$ decays as $1/x^{1+\alpha}$ with $\alpha<2$ for large $x$. We give here a glimpse of Levy flights in physics through two examples, without going into technical details. We first introduce a simple toy model, the Arrhenius cascade. We then present an important physical process, subrecoil laser cooling of atomic gases, in which Levy flights play an essential role.