▎ 摘　　要

We present a theoretical analysis of the relaxation cascade of a photoexcited electron in graphene in the presence of screened electron-electron interaction in the random phase approximation. We calculate the relaxation rate of high energy electrons and the jump-size distribution of the random walk constituting the cascade which exhibits fat tails. We find that the statistics of the entire cascade are described by Levy flights with constant drift instead of standard drift diffusion in energy space. The Levy flight manifests nontrivial scaling relations of the fluctuations in the cascade time, which is related to the problem of the first passage time of Levy processes. Furthermore we determine the transient differential transmission of graphene after an excitation by a laser pulse taking into account the fractional kinetics of the relaxation dynamics.