Do we observe L\'evy flights in cosmic rays?

Abstract

We argue that the so called long flying component (LFC) observed in some cosmic ray experiments are yet another manifestation of L\'evy distributions (with index $q=1.3$), this time of the distribution observation probability of the depths of starting points of cascades. It means that LFC is governed by the so called long-tail L\'evy-like anomalous superdiffusion, a phenomenon frequently encountered in Nature. Its connection with the so called Tsallis's statistics is also briefly discussed.